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Question: initial condition over a range for a pde

Question:initial condition over a range for a pde

John Brew 37 Maple
derivative coordinates
April 16 2007
1
This is probably very elementary, but I am a new Maple user (first day) and would appreciate any help. I am using Maple 11. I am trying to solve Laplace's equation in a circle and so have set up the pde in polar coordinates. pde := Diff(u(r, theta), r, r)+(Diff(u(r, theta), r))/r+(Diff(u(r, theta), theta, theta))/r^2 = 0 My problem is that I want to specify initial conditions over a range. i.e. u(r,theta)=1 for r=0.5 to 1 for theta=0 and theta=2*pi, and u(r,theta)=-1 for r=0.5 to 1 for theta=pi. My problem is that I don't know how to specify the condition for a limited part of the r range. (I will also need to specify a derivative condition for r=1 and all theta, but this seems straightforward.) I shall be very grateful to anyone who who can offer any help on this.
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