1. Consider the following problem defined on a semi-infinite interval, a2 azu azu 0 0 0x2 at2 u(0, t) = (sin(t) Osts 2n 0 otherwise lim u(x, t) = 0 x+00 u(x, 0) = 0 ut (x, 0) = 0 (a) Describe a possible scenario where the above partial differential equation together with the initial and boundary conditions would be a good model (b) Use the Laplace transform with respect to t to solve the given problem (c) Solve problem 1, but now over the infinite interval -co