Consider the heat equation with periodic boundary condintion; u x = ku xx -l < x
ID: 2966567 • Letter: C
Question
Consider the heat equation with periodic boundary condintion;
ux = kuxx -l < x < l, t >0,
u(-l,t) = u(l,t) t > 0,
ux(-l,t) = ux(l,t) t > 0,
u(x,0) = f(x).
a) Give a physical interpretation for each line in the problem.
b) State the eigenvalue problem for X.
c) Analyzing the 3 cases for the sign of lambda, determine the eigenvalues and the eigenfunctions for the X problem.
d) Use lambda in (c), solve the T problem.
e) Use the Superposition Principle to obtain the general solution of the givena initial - boundary value problem as an infinite series.
Explanation / Answer
(c) # Analyzing the 3 cases for the sign of lambda, determine the eigenvalues and the eigenfunctions for the X problem.