PDE-Examples

PDE-Examples - u x = v y , u y =-v x Maxwells equations in...

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Math 425, Spring 2011 Jerry L. Kazdan Classical Examples of PDEs Laplace equation: Δ u : = 3 j = 1 2 u x 2 j = 0 (some write Δ u = · u = 2 u ) Poisson equation: - Δ u = f ( x ) Helmholtz (or eigenvalue) equation: - Δ u = λ u Transport equation: u t = 3 j = 1 b j u x j Heat (or diffusion) equation: u t - k Δ u = 0 Schr¨odinger equation iu t = - Δ u + V ( x ) u Wave equation: u tt - c 2 Δ u = 0 Cauchy-Riemann equations:
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Unformatted text preview: u x = v y , u y =-v x Maxwells equations in a vacuum: E t = c H , H t =-c E , div H = , div E = Eulers (nonlinear) equations for incompressible inviscid ow: u t + u u =- p , div u =...
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This note was uploaded on 03/06/2012 for the course MATH 260 taught by Professor Staff during the Spring '12 term at UPenn.

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