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- Ján Filo, Volker Pluschke
- 2006

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 ux = vx , 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… (More)

- Ján Filo, Volker Pluschke
- SIAM J. Math. Analysis
- 2002

Abstract. We investigate a parabolic-elliptic problem, where the time derivative is multiplied by a coefficient which may vanish on time-dependent spatial subdomains. The linear equation is supplemented by a nonlinear Neumann boundary condition −∂u/∂νA = g(·, ·, u) with a locally defined, Lr-bounded function g(t, ·, ξ). We prove the existence of a local… (More)

- Volker Pluschke
- 1996

In the paper we investigate local existence of a weak solution u to a degenerate parabolic boundary value problem. Degeneration occurs in the coeecient g(x; t; u) in front of the time derivative which is not assumed to be bounded below by some positive constant. Moreover, this coeecient depends on the solution u. We approximate the problem by… (More)

- Volker Pluschke
- 2001

In this paper we study a free{boundary problem in a multicomponent domain. Our study was motivated by the mathematical modelling of dermal and transdermal drug delivery, where the multilayered skin model was considered. At the interface connecting two components the conservation of the ux and Nernst's distribution law hold and it is supposed that in any… (More)

- Wolfgang Seifert, Volker Pluschke
- Materials
- 2012

In the classical theory of thermoelectricity, the performance integrals for a fully self-compatible material depend on the dimensionless figure of merit zT. Usually these integrals are evaluated for constraints z = const. and zT = const., respectively. In this paper we discuss the question from a mathematical point of view whether there is an optimal… (More)

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