MAT 118A Study Guide - Final Guide: Unit Disk, Dirichlet Problem, Open Set
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Unless stated otherwise, you use standard results from lectures or the text provided you state them clearly. 1: [20 pts] for each of the following pdes for u(x, y), give their order and say if they are nonlinear or linear. If they are linear, say if they are homogeneous or nonhomogeneous and if they have constant or variable coe cients. (a) ux = (sin x)uy (b) uux + uy = uxx + sin x (c) uxxyy = sin x. 2: [30 pts] solve the following initial value problem for u(x, t): ut + 3ux = sin t, u(x, 0) = sin x. [30 pts] (a) solve the following initial-boundary value problem for the. 3. heat equation for u(x, t): ut = uxx ux(0, t) = 0, u(x, 0) = f (x) 0 < x < 1, ux(1, t) = 0,
