Using Fourier Transform in $x$, find the solution $ u(x,t) $ to the PDE
$ u_t = c^2u_{xx} - hu$
with the initial conditions
$ u(x,0) = e^{-x^2} (-\infty < x< \infty)$
Could someone guide me through how to set up this problem?
1D Heat Equation, Non-Insulated Infinite Bar
1
$\begingroup$
pde
fourier-transform
heat-equation
1 Answers
0
Make the change $v=e^{ht}u$ and get the heat equation for $v$.