Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Homework 9

Math 442: Intro to Partial Differential Equations

(Exercises are taken from Partial Differential Equations An Introduction, Second Edition by Walter A. Strauss.)

1. Find the solution to

ut = uxx − xux, u(0, x) = x2

2. Exercise §10.3 #5. Solve the diffusion equation in the ball of radius a, with u= B on the boundary and u= C when t= 0, where B and C are constants. (Hint: The answer is radial.)

3. Exercise §9.4 #4. Derive the first four Hermite polynomials from scratch.