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**Unformatted text preview: **f LocT/wm g —————__l._._ MATH 412: Problem Set 2
due Thursday, February 7, 2008 1. Strauss 2.2 #2 - energy and momentum for wave equation
2. Strauss 2.2 #5 — damped wave equation 3. Consider the following transport-decay equation for Mrs, t):
at + can: 2 —,\u Where A > D is a constant. By making an appropriate change of variables similar to
What we discussed in class, convert this to an ordinary differential equation (ODE).
Then solve that equation, remembering that any constants could be functions of the
other variable. From this obtain a solution ii(rr:, t). Show also that this equation can be solved by making the following change of dependent
variable (the function itself): w(m,t) = n(a‘,t)e)‘t How do you interpret this? 4. Strauss 2.3 #6 - comparison principle for heat equation HINT: deﬁne w(mj t) : nix, t) — ii(:r, t), and use the Maximum Principle for the heat
equation (p.42) 5. Strauss 2.3 #8 - radiative boundary condition
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