Solving partial differential equation. The 2019 Stack Overflow Developer Survey Results Are Inhow to solve $ partial u over partial t - k partial ^2 u over partial x^2 =0$Solving a simple partial differential equationSolving Simple Partial Differential EquationSolve a general partial differential equationHow can I actually solve this kind of partial differential equations?Particular integral of linear partial differential equationParticular integral of Partial DIfferential EquationSolving differential equation without finding integrating factorSolving partial integro-differential equation with symmetrySolving Higher Order Partial Differential Equation
Is it safe to harvest rainwater that fell on solar panels?
RequirePermission not working
Dropping list elements from nested list after evaluation
Why are there uneven bright areas in this photo of black hole?
How to obtain a position of last non-zero element
How do you keep chess fun when your opponent constantly beats you?
Why not take a picture of a closer black hole?
writing variables above the numbers in tikz picture
Deal with toxic manager when you can't quit
Why isn't the circumferential light around the M87 black hole's event horizon symmetric?
Button changing its text & action. Good or terrible?
Falsification in Math vs Science
Short story: child made less intelligent and less attractive
What is this sharp, curved notch on my knife for?
Why can't devices on different VLANs, but on the same subnet, communicate?
Likelihood that a superbug or lethal virus could come from a landfill
What information about me do stores get via my credit card?
How do I free up internal storage if I don't have any apps downloaded?
Worn-tile Scrabble
Keeping a retro style to sci-fi spaceships?
Is an up-to-date browser secure on an out-of-date OS?
The phrase "to the numbers born"?
What does もの mean in this sentence?
Is Cinnamon a desktop environment or a window manager? (Or both?)
Solving partial differential equation.
The 2019 Stack Overflow Developer Survey Results Are Inhow to solve $ partial u over partial t - k partial ^2 u over partial x^2 =0$Solving a simple partial differential equationSolving Simple Partial Differential EquationSolve a general partial differential equationHow can I actually solve this kind of partial differential equations?Particular integral of linear partial differential equationParticular integral of Partial DIfferential EquationSolving differential equation without finding integrating factorSolving partial integro-differential equation with symmetrySolving Higher Order Partial Differential Equation
$begingroup$
I want to solve this kind of equation: $$A∂f(x, t)over ∂t = Bd^2f(x, t)over mathrm dx^2$$ I tried to solve this equation in this way: $f(x, t) = a(x)b(t)$. But can I solve this more general?
calculus pde partial-derivative
edited Mar 24 at 7:10
MarianD
2,2611618
asked Mar 24 at 6:47
Svyatoslav TymykSvyatoslav Tymyk
41
$endgroup$
add a comment |
$begingroup$
I want to solve this kind of equation: $$A∂f(x, t)over ∂t = Bd^2f(x, t)over mathrm dx^2$$ I tried to solve this equation in this way: $f(x, t) = a(x)b(t)$. But can I solve this more general?
calculus pde partial-derivative
edited Mar 24 at 7:10
MarianD
2,2611618
asked Mar 24 at 6:47
Svyatoslav TymykSvyatoslav Tymyk
41
$endgroup$
$begingroup$
Hi and welcome to MSE! I want to remind you that it is generally preferred you include context when asking a question here (which can include: where this problem came from, your own attempts, and a specific idea as to where you're stuck) - it also lets us help you better! As is, your question is little more than an isolated problem, and thus likely to get a lot of downvotes and closed. Feel free to edit the context into your post though! Here's a useful link: asking a good question.
$endgroup$
– Eevee Trainer
Mar 24 at 6:50
$begingroup$
this is heat PDE. Use separation of variables as you started. Need boundary and initial condition. There are many examples on the internet of how to solve this. without boundary conditions given, you can't obtain solution, since the form of the solution depends on type of boundary conditions.
$endgroup$
– Nasser
Mar 24 at 6:52
$begingroup$
Sorry, yes I have boundary condition here. I know that $f(0) = 0$ and $f(x, 0) = g(x)$
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:57
$begingroup$
so you are saying this is a semi-infinite domain? i.e. for $0<x<infty$? You need to specify complete and exact specification of the PDE. Also not a good idea to use $f$ for the dependent variable. a common symbol is $u$
$endgroup$
– Nasser
Mar 24 at 7:01
$begingroup$
You should include any boundary and initial conditions into the question since they provide context
$endgroup$
– Dylan
Mar 24 at 7:16
add a comment |
$begingroup$
I want to solve this kind of equation: $$A∂f(x, t)over ∂t = Bd^2f(x, t)over mathrm dx^2$$ I tried to solve this equation in this way: $f(x, t) = a(x)b(t)$. But can I solve this more general?
calculus pde partial-derivative
edited Mar 24 at 7:10
MarianD
2,2611618
asked Mar 24 at 6:47
Svyatoslav TymykSvyatoslav Tymyk
41
$endgroup$
I want to solve this kind of equation: $$A∂f(x, t)over ∂t = Bd^2f(x, t)over mathrm dx^2$$ I tried to solve this equation in this way: $f(x, t) = a(x)b(t)$. But can I solve this more general?
calculus pde partial-derivative
calculus pde partial-derivative
edited Mar 24 at 7:10
MarianD
2,2611618
asked Mar 24 at 6:47
Svyatoslav TymykSvyatoslav Tymyk
41
edited Mar 24 at 7:10
MarianD
2,2611618
asked Mar 24 at 6:47
Svyatoslav TymykSvyatoslav Tymyk
41
edited Mar 24 at 7:10
MarianD
2,2611618
edited Mar 24 at 7:10
MarianD
2,2611618
edited Mar 24 at 7:10
MarianD
2,2611618
2,2611618
asked Mar 24 at 6:47
Svyatoslav TymykSvyatoslav Tymyk
41
asked Mar 24 at 6:47
Svyatoslav TymykSvyatoslav Tymyk
41
asked Mar 24 at 6:47
Svyatoslav TymykSvyatoslav Tymyk
41
41
$begingroup$
Hi and welcome to MSE! I want to remind you that it is generally preferred you include context when asking a question here (which can include: where this problem came from, your own attempts, and a specific idea as to where you're stuck) - it also lets us help you better! As is, your question is little more than an isolated problem, and thus likely to get a lot of downvotes and closed. Feel free to edit the context into your post though! Here's a useful link: asking a good question.
$endgroup$
– Eevee Trainer
Mar 24 at 6:50
$begingroup$
this is heat PDE. Use separation of variables as you started. Need boundary and initial condition. There are many examples on the internet of how to solve this. without boundary conditions given, you can't obtain solution, since the form of the solution depends on type of boundary conditions.
$endgroup$
– Nasser
Mar 24 at 6:52
$begingroup$
Sorry, yes I have boundary condition here. I know that $f(0) = 0$ and $f(x, 0) = g(x)$
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:57
$begingroup$
so you are saying this is a semi-infinite domain? i.e. for $0<x<infty$? You need to specify complete and exact specification of the PDE. Also not a good idea to use $f$ for the dependent variable. a common symbol is $u$
$endgroup$
– Nasser
Mar 24 at 7:01
$begingroup$
You should include any boundary and initial conditions into the question since they provide context
$endgroup$
– Dylan
Mar 24 at 7:16
add a comment |
$begingroup$
Hi and welcome to MSE! I want to remind you that it is generally preferred you include context when asking a question here (which can include: where this problem came from, your own attempts, and a specific idea as to where you're stuck) - it also lets us help you better! As is, your question is little more than an isolated problem, and thus likely to get a lot of downvotes and closed. Feel free to edit the context into your post though! Here's a useful link: asking a good question.
$endgroup$
– Eevee Trainer
Mar 24 at 6:50
$begingroup$
this is heat PDE. Use separation of variables as you started. Need boundary and initial condition. There are many examples on the internet of how to solve this. without boundary conditions given, you can't obtain solution, since the form of the solution depends on type of boundary conditions.
$endgroup$
– Nasser
Mar 24 at 6:52
$begingroup$
Sorry, yes I have boundary condition here. I know that $f(0) = 0$ and $f(x, 0) = g(x)$
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:57
$begingroup$
so you are saying this is a semi-infinite domain? i.e. for $0<x<infty$? You need to specify complete and exact specification of the PDE. Also not a good idea to use $f$ for the dependent variable. a common symbol is $u$
$endgroup$
– Nasser
Mar 24 at 7:01
$begingroup$
You should include any boundary and initial conditions into the question since they provide context
$endgroup$
– Dylan
Mar 24 at 7:16
$begingroup$
Hi and welcome to MSE! I want to remind you that it is generally preferred you include context when asking a question here (which can include: where this problem came from, your own attempts, and a specific idea as to where you're stuck) - it also lets us help you better! As is, your question is little more than an isolated problem, and thus likely to get a lot of downvotes and closed. Feel free to edit the context into your post though! Here's a useful link: asking a good question.
$endgroup$
– Eevee Trainer
Mar 24 at 6:50
$begingroup$
Hi and welcome to MSE! I want to remind you that it is generally preferred you include context when asking a question here (which can include: where this problem came from, your own attempts, and a specific idea as to where you're stuck) - it also lets us help you better! As is, your question is little more than an isolated problem, and thus likely to get a lot of downvotes and closed. Feel free to edit the context into your post though! Here's a useful link: asking a good question.
$endgroup$
– Eevee Trainer
Mar 24 at 6:50
$begingroup$
this is heat PDE. Use separation of variables as you started. Need boundary and initial condition. There are many examples on the internet of how to solve this. without boundary conditions given, you can't obtain solution, since the form of the solution depends on type of boundary conditions.
$endgroup$
– Nasser
Mar 24 at 6:52
$begingroup$
this is heat PDE. Use separation of variables as you started. Need boundary and initial condition. There are many examples on the internet of how to solve this. without boundary conditions given, you can't obtain solution, since the form of the solution depends on type of boundary conditions.
$endgroup$
– Nasser
Mar 24 at 6:52
$begingroup$
Sorry, yes I have boundary condition here. I know that $f(0) = 0$ and $f(x, 0) = g(x)$
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:57
$begingroup$
Sorry, yes I have boundary condition here. I know that $f(0) = 0$ and $f(x, 0) = g(x)$
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:57
$begingroup$
so you are saying this is a semi-infinite domain? i.e. for $0<x<infty$? You need to specify complete and exact specification of the PDE. Also not a good idea to use $f$ for the dependent variable. a common symbol is $u$
$endgroup$
– Nasser
Mar 24 at 7:01
$begingroup$
so you are saying this is a semi-infinite domain? i.e. for $0<x<infty$? You need to specify complete and exact specification of the PDE. Also not a good idea to use $f$ for the dependent variable. a common symbol is $u$
$endgroup$
– Nasser
Mar 24 at 7:01
$begingroup$
You should include any boundary and initial conditions into the question since they provide context
$endgroup$
– Dylan
Mar 24 at 7:16
$begingroup$
You should include any boundary and initial conditions into the question since they provide context
$endgroup$
– Dylan
Mar 24 at 7:16
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
If $A,B$ are just (nonzero) constants (i.e., this is just a heat equation), then yes it can be solved in other ways. For example, the Fourier transform would do the trick.
If $A,B$ aren't constants, then I'd need some more info on them in order to give you an answer.
Edit: If you're aim is to solve the BVP, then the approach you mention (separation of variables) is probably the way to go. In some domains (including an interval as in your example) you can use a Green function, but you'll probably have to use separation of variables to solve for it, so I'm not sure you're going to escape that approach in the long run.
answered Mar 24 at 6:56
Gary MoonGary Moon
921127
$endgroup$
$begingroup$
They are pure, nonzero constants. And the boundary are $f(0) = 0$, $f(x, 0) = g(x)$.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:59
$begingroup$
You mean $f(0,t)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:05
$begingroup$
No, in my case $f(x, 0) = sin(πx/a)$, where $a$ is just nonzero constant.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 7:09
$begingroup$
I understand you have an inhomogeneous IC. I was just trying to get at what you meant by $f(0)=0$. Does the problem have homogeneous BCs?
$endgroup$
– Gary Moon
Mar 24 at 7:24
2
$begingroup$
Then, what do you mean by $f(0)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:59
|
show 2 more comments
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3160208%2fsolving-partial-differential-equation%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If $A,B$ are just (nonzero) constants (i.e., this is just a heat equation), then yes it can be solved in other ways. For example, the Fourier transform would do the trick.
If $A,B$ aren't constants, then I'd need some more info on them in order to give you an answer.
Edit: If you're aim is to solve the BVP, then the approach you mention (separation of variables) is probably the way to go. In some domains (including an interval as in your example) you can use a Green function, but you'll probably have to use separation of variables to solve for it, so I'm not sure you're going to escape that approach in the long run.
answered Mar 24 at 6:56
Gary MoonGary Moon
921127
$endgroup$
$begingroup$
They are pure, nonzero constants. And the boundary are $f(0) = 0$, $f(x, 0) = g(x)$.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:59
$begingroup$
You mean $f(0,t)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:05
$begingroup$
No, in my case $f(x, 0) = sin(πx/a)$, where $a$ is just nonzero constant.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 7:09
$begingroup$
I understand you have an inhomogeneous IC. I was just trying to get at what you meant by $f(0)=0$. Does the problem have homogeneous BCs?
$endgroup$
– Gary Moon
Mar 24 at 7:24
2
$begingroup$
Then, what do you mean by $f(0)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:59
|
show 2 more comments
$begingroup$
If $A,B$ are just (nonzero) constants (i.e., this is just a heat equation), then yes it can be solved in other ways. For example, the Fourier transform would do the trick.
If $A,B$ aren't constants, then I'd need some more info on them in order to give you an answer.
Edit: If you're aim is to solve the BVP, then the approach you mention (separation of variables) is probably the way to go. In some domains (including an interval as in your example) you can use a Green function, but you'll probably have to use separation of variables to solve for it, so I'm not sure you're going to escape that approach in the long run.
answered Mar 24 at 6:56
Gary MoonGary Moon
921127
$endgroup$
$begingroup$
They are pure, nonzero constants. And the boundary are $f(0) = 0$, $f(x, 0) = g(x)$.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:59
$begingroup$
You mean $f(0,t)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:05
$begingroup$
No, in my case $f(x, 0) = sin(πx/a)$, where $a$ is just nonzero constant.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 7:09
$begingroup$
I understand you have an inhomogeneous IC. I was just trying to get at what you meant by $f(0)=0$. Does the problem have homogeneous BCs?
$endgroup$
– Gary Moon
Mar 24 at 7:24
2
$begingroup$
Then, what do you mean by $f(0)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:59
|
show 2 more comments
$begingroup$
If $A,B$ are just (nonzero) constants (i.e., this is just a heat equation), then yes it can be solved in other ways. For example, the Fourier transform would do the trick.
If $A,B$ aren't constants, then I'd need some more info on them in order to give you an answer.
Edit: If you're aim is to solve the BVP, then the approach you mention (separation of variables) is probably the way to go. In some domains (including an interval as in your example) you can use a Green function, but you'll probably have to use separation of variables to solve for it, so I'm not sure you're going to escape that approach in the long run.
answered Mar 24 at 6:56
Gary MoonGary Moon
921127
$endgroup$
If $A,B$ are just (nonzero) constants (i.e., this is just a heat equation), then yes it can be solved in other ways. For example, the Fourier transform would do the trick.
If $A,B$ aren't constants, then I'd need some more info on them in order to give you an answer.
Edit: If you're aim is to solve the BVP, then the approach you mention (separation of variables) is probably the way to go. In some domains (including an interval as in your example) you can use a Green function, but you'll probably have to use separation of variables to solve for it, so I'm not sure you're going to escape that approach in the long run.
answered Mar 24 at 6:56
Gary MoonGary Moon
921127
edited Mar 24 at 7:21
answered Mar 24 at 6:56
Gary MoonGary Moon
921127
answered Mar 24 at 6:56
Gary MoonGary Moon
921127
answered Mar 24 at 6:56
Gary MoonGary Moon
921127
921127
$begingroup$
They are pure, nonzero constants. And the boundary are $f(0) = 0$, $f(x, 0) = g(x)$.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:59
$begingroup$
You mean $f(0,t)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:05
$begingroup$
No, in my case $f(x, 0) = sin(πx/a)$, where $a$ is just nonzero constant.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 7:09
$begingroup$
I understand you have an inhomogeneous IC. I was just trying to get at what you meant by $f(0)=0$. Does the problem have homogeneous BCs?
$endgroup$
– Gary Moon
Mar 24 at 7:24
2
$begingroup$
Then, what do you mean by $f(0)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:59
|
show 2 more comments
$begingroup$
They are pure, nonzero constants. And the boundary are $f(0) = 0$, $f(x, 0) = g(x)$.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:59
$begingroup$
You mean $f(0,t)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:05
$begingroup$
No, in my case $f(x, 0) = sin(πx/a)$, where $a$ is just nonzero constant.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 7:09
$begingroup$
I understand you have an inhomogeneous IC. I was just trying to get at what you meant by $f(0)=0$. Does the problem have homogeneous BCs?
$endgroup$
– Gary Moon
Mar 24 at 7:24
2
$begingroup$
Then, what do you mean by $f(0)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:59
$begingroup$
They are pure, nonzero constants. And the boundary are $f(0) = 0$, $f(x, 0) = g(x)$.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:59
$begingroup$
They are pure, nonzero constants. And the boundary are $f(0) = 0$, $f(x, 0) = g(x)$.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:59
$begingroup$
You mean $f(0,t)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:05
$begingroup$
You mean $f(0,t)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:05
$begingroup$
No, in my case $f(x, 0) = sin(πx/a)$, where $a$ is just nonzero constant.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 7:09
$begingroup$
No, in my case $f(x, 0) = sin(πx/a)$, where $a$ is just nonzero constant.
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 7:09
$begingroup$
I understand you have an inhomogeneous IC. I was just trying to get at what you meant by $f(0)=0$. Does the problem have homogeneous BCs?
$endgroup$
– Gary Moon
Mar 24 at 7:24
$begingroup$
I understand you have an inhomogeneous IC. I was just trying to get at what you meant by $f(0)=0$. Does the problem have homogeneous BCs?
$endgroup$
– Gary Moon
Mar 24 at 7:24
2
2
$begingroup$
Then, what do you mean by $f(0)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:59
$begingroup$
Then, what do you mean by $f(0)=0$?
$endgroup$
– Gary Moon
Mar 24 at 7:59
|
show 2 more comments
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3160208%2fsolving-partial-differential-equation%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Hi and welcome to MSE! I want to remind you that it is generally preferred you include context when asking a question here (which can include: where this problem came from, your own attempts, and a specific idea as to where you're stuck) - it also lets us help you better! As is, your question is little more than an isolated problem, and thus likely to get a lot of downvotes and closed. Feel free to edit the context into your post though! Here's a useful link: asking a good question.
$endgroup$
– Eevee Trainer
Mar 24 at 6:50
$begingroup$
this is heat PDE. Use separation of variables as you started. Need boundary and initial condition. There are many examples on the internet of how to solve this. without boundary conditions given, you can't obtain solution, since the form of the solution depends on type of boundary conditions.
$endgroup$
– Nasser
Mar 24 at 6:52
$begingroup$
Sorry, yes I have boundary condition here. I know that $f(0) = 0$ and $f(x, 0) = g(x)$
$endgroup$
– Svyatoslav Tymyk
Mar 24 at 6:57
$begingroup$
so you are saying this is a semi-infinite domain? i.e. for $0<x<infty$? You need to specify complete and exact specification of the PDE. Also not a good idea to use $f$ for the dependent variable. a common symbol is $u$
$endgroup$
– Nasser
Mar 24 at 7:01
$begingroup$
You should include any boundary and initial conditions into the question since they provide context
$endgroup$
– Dylan
Mar 24 at 7:16