Unformatted text preview: 4. Concerning 18.3:6: we already did several parts of this problem in which the boundary conditions were homogeneous; the ones I have chosen here are inhomogeneous. You can use any method that you like, but I think that the clearest one is the method I outlined in class: Find the steady-state solution v ( x ) of the equation and boundary conditions (the book usually calls this u s ( x )), so that w ( x, t ) = u ( x, t )-v ( x ) will satisfy a homogeneous boundary value problem which you already know how to solve. 5. 18.3:10. Here you just have to ±nd the steady state solutions; part (c) is particularly illuminating (note that it is closely related to 18.3:6(i)). If you were asked to solve an initial value problem, you could use the steady-state to do so (method outlined in remark 3 above)....
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- Fall '08
- Math, Boundary value problem, Boundary conditions, nonseparated boundary conditions