Reference no: EM132330915

Questions -

Q1. Consider the heat equation u_t = ku_xx defined for 0 ≤ x ≤ L with initial condition u(x, 0) = c and boundary conditions u_x(0, t) = u_x(L, t) = 0. Find a solution satisfying the heat equation with these initial and boundary conditions. Describe the physical meaning of the PDE and of the solution.

Q2. Consider the heat equation u_t = ku_xx for 0 ≤ x ≤ 1 with initial condition u(x, 0) = sin(πx) and boundary conditions u(0, t) = u(1, t) = 0. Show that u(x, t) e^{-kπ^2t} sin(πx) is a solution. Describe the physical meaning of the PDE and of the solution.