Abstract
We consider a system of two porous medium equations defined on two different components of the real line, which are connected by the nonlinear contact condition u x = v x , v = ψ ( u ) on the contact line S . First we prove existence and uniqueness of a solution ( u , v ) on a bounded domain. Furthermore, we are interested in the behaviour of the interface of the porous medium equation when it crosses the contact line S between the two components. To this end we solve the Cauchy problem on unbounded components, consider self-similar solutions for special ψ ( u ) = M u ω and derive a formula for the shape of the interface in that case.
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