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Application of PDE on physicis

  1. Dec 24, 2013 #1
    I want to find some application of the laplace equation on semi-infinite plate on physics
    where the PDE is looke like
    $$u_{xx}+u_{yy}=f , for a<x<\infty , c<y<d$$
    $$u(a,y)=g(y), u(x,c)=f_{1}(x), u(x,d)=f_{2}(x)$$
    $$\lim_{x->\infty} f(x)=\lim_{x->\infty} f_{1}(x)=\lim_{x->\infty} f_{2}(x)=0 $$
    Thank you :)
  2. jcsd
  3. Dec 24, 2013 #2
    One possible physical situation that equations of this form could be consistent with is a steady state conductive heat transfer problem in which the temperature distributions are fixed along the edges, and heat is being generated within the plate (as characterized by the function f(x,y)). In this case u is temperature, or temperature relative to some reference state (e.g., u = 0 at x->∞).
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