How can I solve this linear partial differential equation of 2 variables with Fourier transform?
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For $xin mathbb{R}$ solve using Fourier transform
$$frac{partial u}{partial t}=kfrac{partial^2 u}{partial x^2}-gamma u,$$
where $k, gamma$ are positive constants and $u(x,t)|_{t=0}=f(x).$
First generally (the result should be in a form of convolution integral), then explicitly with $f(x)=e^{-x^2}.$
pde fourier-transform linear-pde
asked Dec 7 '18 at 9:37
Marek OtypkaMarek Otypka
113
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add a comment |
$begingroup$
For $xin mathbb{R}$ solve using Fourier transform
$$frac{partial u}{partial t}=kfrac{partial^2 u}{partial x^2}-gamma u,$$
where $k, gamma$ are positive constants and $u(x,t)|_{t=0}=f(x).$
First generally (the result should be in a form of convolution integral), then explicitly with $f(x)=e^{-x^2}.$
pde fourier-transform linear-pde
asked Dec 7 '18 at 9:37
Marek OtypkaMarek Otypka
113
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What did you try?
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– Botond
Dec 7 '18 at 10:09
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Fourier transform, but I didn't manage to make it to the step with convolution integral.
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– Marek Otypka
Dec 21 '18 at 13:56
$begingroup$
Please include your work in the question.
$endgroup$
– Botond
Dec 21 '18 at 15:05
add a comment |
$begingroup$
For $xin mathbb{R}$ solve using Fourier transform
$$frac{partial u}{partial t}=kfrac{partial^2 u}{partial x^2}-gamma u,$$
where $k, gamma$ are positive constants and $u(x,t)|_{t=0}=f(x).$
First generally (the result should be in a form of convolution integral), then explicitly with $f(x)=e^{-x^2}.$
pde fourier-transform linear-pde
asked Dec 7 '18 at 9:37
Marek OtypkaMarek Otypka
113
$endgroup$
For $xin mathbb{R}$ solve using Fourier transform
$$frac{partial u}{partial t}=kfrac{partial^2 u}{partial x^2}-gamma u,$$
where $k, gamma$ are positive constants and $u(x,t)|_{t=0}=f(x).$
First generally (the result should be in a form of convolution integral), then explicitly with $f(x)=e^{-x^2}.$
pde fourier-transform linear-pde
pde fourier-transform linear-pde
asked Dec 7 '18 at 9:37
Marek OtypkaMarek Otypka
113
asked Dec 7 '18 at 9:37
Marek OtypkaMarek Otypka
113
edited Dec 7 '18 at 9:47
Marek Otypka
asked Dec 7 '18 at 9:37
Marek OtypkaMarek Otypka
113
asked Dec 7 '18 at 9:37
Marek OtypkaMarek Otypka
113
asked Dec 7 '18 at 9:37
Marek OtypkaMarek Otypka
113
113
$begingroup$
What did you try?
$endgroup$
– Botond
Dec 7 '18 at 10:09
$begingroup$
Fourier transform, but I didn't manage to make it to the step with convolution integral.
$endgroup$
– Marek Otypka
Dec 21 '18 at 13:56
$begingroup$
Please include your work in the question.
$endgroup$
– Botond
Dec 21 '18 at 15:05
add a comment |
$begingroup$
What did you try?
$endgroup$
– Botond
Dec 7 '18 at 10:09
$begingroup$
Fourier transform, but I didn't manage to make it to the step with convolution integral.
$endgroup$
– Marek Otypka
Dec 21 '18 at 13:56
$begingroup$
Please include your work in the question.
$endgroup$
– Botond
Dec 21 '18 at 15:05
$begingroup$
What did you try?
$endgroup$
– Botond
Dec 7 '18 at 10:09
$begingroup$
What did you try?
$endgroup$
– Botond
Dec 7 '18 at 10:09
$begingroup$
Fourier transform, but I didn't manage to make it to the step with convolution integral.
$endgroup$
– Marek Otypka
Dec 21 '18 at 13:56
$begingroup$
Fourier transform, but I didn't manage to make it to the step with convolution integral.
$endgroup$
– Marek Otypka
Dec 21 '18 at 13:56
$begingroup$
Please include your work in the question.
$endgroup$
– Botond
Dec 21 '18 at 15:05
$begingroup$
Please include your work in the question.
$endgroup$
– Botond
Dec 21 '18 at 15:05
add a comment |
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$begingroup$
What did you try?
$endgroup$
– Botond
Dec 7 '18 at 10:09
$begingroup$
Fourier transform, but I didn't manage to make it to the step with convolution integral.
$endgroup$
– Marek Otypka
Dec 21 '18 at 13:56
$begingroup$
Please include your work in the question.
$endgroup$
– Botond
Dec 21 '18 at 15:05