Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4612742 | Journal of Differential Equations | 2009 | 30 Pages |
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 conditionux=vx,v=ψ(u)on the contact lineS. First we prove existence and uniqueness of a solution (u,v)(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)=Muωψ(u)=Muω and derive a formula for the shape of the interface in that case.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Ján Filo, Volker Pluschke,