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Can you recommend me a good site/textbook explaining how to solve and simulate Partial Differential Equations where the contour is not fixed, but can vary with time?

I'm interested both to the case where the shape of the contour is a function of time, and to the case where the shape depends on the various components of the system.

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Are you referring to "Free boundary problems"? –  Robert Israel Oct 19 '12 at 5:30
    
I'm by no means expert on the matter, but I remember that continuum mechanics formulate equilibrium equations with movable boundaries, and they do remove time dependency in the domain. A quick look to Fung's First Course in Continuum Mechanics might give you basic insight. –  Pragabhava Oct 19 '12 at 7:03
    
@Pragabhava thanks. I think that I mean a free boundary problem, but I am not sure.. I had a quick look on wikipedia en.wikipedia.org/wiki/Free_boundary_problem and it seems that if I can set $\Omega \equiv \Gamma$ then yes I mean that. I will have a look at your reference! –  lucacerone Oct 19 '12 at 7:52

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