1. Consider the first order PDE,
∂u/∂t = ct(∂u/∂x) -∞ < x < ∞ c does not equal 0
a) Find the fundamental solution
b) Use the fundamental solution and convolution to find a formula for the solution to:
∂u/∂t = ct(∂u/∂x) -∞ < x < ∞ c does not equal 0 u(x,0) = f(x)
c) Use the method of characteristics to find the solution to part b.(Make sure your answers agree)
This finds the fundamental solution of a first-order partial differential equation, and uses that solution and convolution, as well as method of characteristics, in another problem.