Question

Let u be the solution to the initial boundary value problem for the Heat Equation, tE (0, o0), те (0, 1); дла(t, г) — 3 Әғu(t, a), with boundary conditions u(t, 0) — 0, и(t, 1) — 0, and with initial condition 0, 1 3 EA 4 u(0, a) f(x) 4. 3 The solution u of the problem above, with the conventions given in class, has the form С сп tn (t) и,(2), u(t, x) - T 1 with the normalization conditions 13 (0) Ча 2n 1. Wn Find the functions v: Wn, and the constants c (2) Ҹа (x)4m Cn

Answer 1

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