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Homework 10

Math 442: Intro to Partial Differential Equations

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

1. Read page 276.

2. Exercise §6.3 #1. Suppose that u is a harmonic function in the disk D = {r < 2} and that u = 3sin(2θ) + 1 for r= 2. Without finding the solution, answer the following questions.

(a) Find the maximum value of u in D.

(b) Calculate the value of u at the origin.

3. Exercise §6.3 #2. Solve uxx + uyy = 0 in the disk {r < a} with the boundary condition

u = 1 + 3sinθ on r = a.