Solve the following problem:
1. The advection equation
∂u/∂t(x,t)=-K(∂u/∂x)(x,t)- ru(x,t) (1)
where K and r > 0 are constants, models a moving and diffusing quantity.
a.) Use the method of characteristics to find the solution to (1) with initial condition u(x,0) = f(x)
b.) Describe qualitatively how the values of K and r change the solution.
1. Use the method of characteristics to solve the first order linear PDE,
∂u/∂t +te-t2(∂u/∂x)= sin(t)u
with our initial bump, u(x, 0) = f(x) = e-x2