Consider the initial value boundary problem presented below, which represents the tempurature u(x, t) of a laterally - insulated metal rod of length L=1
PDE: ut = a^2 uxx O≤ t ≤ 1, 0 Boundary conditions: {u(0,t)=1 {u(1,t)=1 0 Initial condition: u(x,0)=1-sin(πx), 0≤x≤1
Describe what happens to the temperature over time and use a graph to ilustrate your reasoning.