Let u be the solution to the initial boundary value problem for the Heat Equation, with...

  

Transcribed Image Text:

Let u be the solution to the initial boundary value problem for the Heat Equation, with Dirichlet boundary conditions u(t,0) = 0 and u(t, 1) = 0, and with initial condition d,u(t, x) = 3 du(t, x), The solution u of the problem above, with the conventions given in class, has the form Cn = 2/(npi)^2sin(npi/2)-1/(npi) cos(npi/2) Σ u(0, x) = f(x) = . Σ u(t, x) = n=1 t€ (0,00), X. 0, XE = [0,1), with the normalization conditions v₂ (0) = 1 and w₁() = 1. Find the functions Un, W₁, and the constants C Un(t) = e^(-4x^2pi^2t) Σ w₁(x) = sin(npix) x € (0, 1); *€ [1]. XE Cn Un(t) wn(x), Let u be the solution to the initial boundary value problem for the Heat Equation, with Dirichlet boundary conditions u(t,0) = 0 and u(t, 1) = 0, and with initial condition d,u(t, x) = 3 du(t, x), The solution u of the problem above, with the conventions given in class, has the form Cn = 2/(npi)^2sin(npi/2)-1/(npi) cos(npi/2) Σ u(0, x) = f(x) = . Σ u(t, x) = n=1 t€ (0,00), X. 0, XE = [0,1), with the normalization conditions v₂ (0) = 1 and w₁() = 1. Find the functions Un, W₁, and the constants C Un(t) = e^(-4x^2pi^2t) Σ w₁(x) = sin(npix) x € (0, 1); *€ [1]. XE Cn Un(t) wn(x),

Answer rating: 100% (QA)

SOLUTION So u t x Up 2 2 C Un 18 un 8 Cn n1 Usi4 Bathic fies th... View the full answer