I have the PDE $u_t-u_{xx}=-u^2$ with boundary conditions $u(0,t)=0$ , $u(a,t)=0$ and $u(x,0)=0$ for $0<x<a$ and $0<t<T$ I have tried to use separation of variables and Fourier's method but can't get anywhere as I cant get past the part where you make both sides equal to a constant. Any help will be appreciated!
2026-03-31 22:29:22.1774996162
Can I use separation of variables?
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