Math 442: Intro to Partial Differential Equations Homework 1
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Homework 1
MATH 442: INTRO TO PARTIAL DIFFERENTIAL EQUATIONS
(Exercises are taken from paTtial DifeTential Equations An IntToduction, second Edition by walter A. strauss.)
1. Exercise &1.1 #1. verify the linearity and non-linearity of the following operators by checking whether or not equations (3) are valid. which of the following operators are linear?
2. Exercise &1.1 井3. For each of the following equations, state the order and whether it is nonlinear, linear in-homogeneous, or linear homogeneous; provide reasons.
3. Exercise &1.5 #1. consider the problem
consisting of an ODE and a pair of boundary conditions. clearly)the function u(x)= O is a solution. Is this solution unique, OT nOt?Does the answer depend on L?
4. Exercise &1.6 #1. what is the type of each of the following equations?
(a) uxx - uxy + 2ug + uyy - 3uyx + 4u = 0
(b) 9uxx + 6uxy + uyy + ux = 0
2023-07-22