I’ve been doing some work on the heat equation recently and I’m having problems with the following equation: $$u_t-\frac{1}{1-t}u_{xx}=0, 0<x<π, t>0$$ with boundary equations: $$u(x,0)=g(x), 0<x<π$$ $$u_x(0,t)=0=u_x(π,t), t \ge 0$$ I know normally I can use separation of variables to solve this. However, I’m unsure as to how to solve this without knowing $g$. Also, I know the Neumann boundary conditions appear periodic, hence my solution must have $\cos(nx)$ in it. However, in all honesty I’m very stuck with this and have been for the past couple hours. How do I go about solving this boundary initial value problem?
2026-04-01 00:05:47.1775001947
Solving the following initial and boundary value problem
33 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in BOUNDARY-VALUE-PROBLEM
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