How do I obtain a solution of this Helmholtz equation? The 2019 Stack Overflow Developer Survey Results Are InSolution to Laplace equation in $mathbbR^n$Kernel of Helmholtz Equation on a planeWhy this abuse of notation correctly solves the heat equationTwo dimensional Helmholtz equation and complex function theoryMean value property for solution of Helmholtz equation(Fundamental) Solution of the Helmholtz equationDeriving the fundamental solution for the Helmholtz operator in $mathbbR$Fundamental solution for 1D nonhomogeneous wave equationHelmholtz equation superpositionFourier transform for Helmholtz equation
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How do I obtain a solution of this Helmholtz equation?
The 2019 Stack Overflow Developer Survey Results Are InSolution to Laplace equation in $mathbbR^n$Kernel of Helmholtz Equation on a planeWhy this abuse of notation correctly solves the heat equationTwo dimensional Helmholtz equation and complex function theoryMean value property for solution of Helmholtz equation(Fundamental) Solution of the Helmholtz equationDeriving the fundamental solution for the Helmholtz operator in $mathbbR$Fundamental solution for 1D nonhomogeneous wave equationHelmholtz equation superpositionFourier transform for Helmholtz equation
$begingroup$
I want to get a solution of the following Helmholtz equation.
$$ Delta u+ k^2 u = f, qquad x in mathbbR^n, ; k>0$$
Using the Fourier transform, I have
beginalign*u&=int_mathbbR^n e^ixcdotxi frac1k^2- int_mathbbR^n e^-iycdotxi f(y)dydxi \
&=int_mathbbR^nf(y)int_mathbbR^n e^i(x-y)cdotxi frac1k^2 - dxi dy.
endalign*
But I can't calculate
$$int_mathbbR^n e^i(x-y)cdotxi frac1k^2 - dxi$$
How do I solve it?
If $n=3$, I probably know the answer that it might be $frace^ik$ although I don't know how it is derived.
integration pde harmonic-analysis linear-pde
edited Mar 24 at 6:51
Rodrigo de Azevedo
13.2k41962
asked Mar 24 at 6:31
IdkwhatIdkwhat
507
$endgroup$
add a comment |
$begingroup$
I want to get a solution of the following Helmholtz equation.
$$ Delta u+ k^2 u = f, qquad x in mathbbR^n, ; k>0$$
Using the Fourier transform, I have
beginalign*u&=int_mathbbR^n e^ixcdotxi frac1k^2- int_mathbbR^n e^-iycdotxi f(y)dydxi \
&=int_mathbbR^nf(y)int_mathbbR^n e^i(x-y)cdotxi frac1k^2 - dxi dy.
endalign*
But I can't calculate
$$int_mathbbR^n e^i(x-y)cdotxi frac1k^2 - dxi$$
How do I solve it?
If $n=3$, I probably know the answer that it might be $frace^ik$ although I don't know how it is derived.
integration pde harmonic-analysis linear-pde
edited Mar 24 at 6:51
Rodrigo de Azevedo
13.2k41962
asked Mar 24 at 6:31
IdkwhatIdkwhat
507
$endgroup$
add a comment |
$begingroup$
I want to get a solution of the following Helmholtz equation.
$$ Delta u+ k^2 u = f, qquad x in mathbbR^n, ; k>0$$
Using the Fourier transform, I have
beginalign*u&=int_mathbbR^n e^ixcdotxi frac1k^2- int_mathbbR^n e^-iycdotxi f(y)dydxi \
&=int_mathbbR^nf(y)int_mathbbR^n e^i(x-y)cdotxi frac1k^2 - dxi dy.
endalign*
But I can't calculate
$$int_mathbbR^n e^i(x-y)cdotxi frac1k^2 - dxi$$
How do I solve it?
If $n=3$, I probably know the answer that it might be $frace^ik$ although I don't know how it is derived.
integration pde harmonic-analysis linear-pde
edited Mar 24 at 6:51
Rodrigo de Azevedo
13.2k41962
asked Mar 24 at 6:31
IdkwhatIdkwhat
507
$endgroup$
I want to get a solution of the following Helmholtz equation.
$$ Delta u+ k^2 u = f, qquad x in mathbbR^n, ; k>0$$
Using the Fourier transform, I have
beginalign*u&=int_mathbbR^n e^ixcdotxi frac1k^2- int_mathbbR^n e^-iycdotxi f(y)dydxi \
&=int_mathbbR^nf(y)int_mathbbR^n e^i(x-y)cdotxi frac1k^2 - dxi dy.
endalign*
But I can't calculate
$$int_mathbbR^n e^i(x-y)cdotxi frac1k^2 - dxi$$
How do I solve it?
If $n=3$, I probably know the answer that it might be $frace^ik$ although I don't know how it is derived.
integration pde harmonic-analysis linear-pde
integration pde harmonic-analysis linear-pde
edited Mar 24 at 6:51
Rodrigo de Azevedo
13.2k41962
asked Mar 24 at 6:31
IdkwhatIdkwhat
507
edited Mar 24 at 6:51
Rodrigo de Azevedo
13.2k41962
asked Mar 24 at 6:31
IdkwhatIdkwhat
507
edited Mar 24 at 6:51
Rodrigo de Azevedo
13.2k41962
edited Mar 24 at 6:51
Rodrigo de Azevedo
13.2k41962
edited Mar 24 at 6:51
Rodrigo de Azevedo
13.2k41962
13.2k41962
asked Mar 24 at 6:31
IdkwhatIdkwhat
507
asked Mar 24 at 6:31
IdkwhatIdkwhat
507
asked Mar 24 at 6:31
IdkwhatIdkwhat
507
507
add a comment |
add a comment |
0
active
oldest
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