PS2 - variable(the function itself w x t = u x t e λt How...

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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 u ( x, t ): u t + cu x = - λu where λ > 0 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 u ( x, t ). Show also that this equation can be solved by making the following change of dependent
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Unformatted text preview: variable (the function itself): w ( x, t ) = u ( x, t ) e λt How do you interpret this? 4. Strauss 2.3 #6 -comparison principle for heat equation HINT: define w ( x, t ) = u ( x, t )-v ( x, t ), and use the Maximum Principle for the heat equation (p.42) 5. Strauss 2.3 #8 -radiative boundary condition 6. Strauss 2.4 #1 -diffusion equation 7. Strauss 2.4 #11 -even and odd initial conditions Version 1.1...
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