Volker Pluschke

A Free Boundary Problem in Dermal Drug Delivery

In this paper we study a free boundary problem in a multicomponent domain. Our study was motivated by the mathematical modeling of dermal and transdermal drug delivery, where the multilayered skin model was considered. At the interface connecting two components the conservation of the flux and Nernsts distribution law hold and it is supposed that in any component there is a positive minimum concentration at which the diffusion front can proceed. The existence of a solution and uniqueness in special cases are shown.

Solution of nonlinear pseudoparabolic equations by semidiscretization in time

In the paper existence theorems for nonlinear pseudoparabolic initial-boundary value problems are proved. To this end there is used the method of semidiscretization in time, where the nonlinear time dependent problem is approximated by a sequence of linear elliptic problems. With assumption of local Lipschitz and Holder-Llpschitz conditions with respect to the nonlinearity there is proved the existence of a unique solution in a sufficiently small time interval and convergence of the approximates to the solution. Furthermore, somewhat weakening the assumptions, a compactness criterion yields convergence of a subsequence of approximates and existence of a solution.

Exact Solution of a Constraint Optimization Problem for the Thermoelectric Figure of Merit

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 temperature characteristics of the figure of merit. We solve this isoperimetric variational problem for the best envelope of a family of curves z(T)T.

An approximation of the axially symmetric flow through a pipe-like domain with a moving part of a boundary

The purpose of this work is to study the existence of solutions for approximation of an unsteady fluid-structure interaction problem. We consider a perturbed Navier-Stokes equation in the cylindrical coordinate system assuming axially symmetric flow. A priori unknown part of the boundary (that interacts with the fluid) is governed with a linear equation of fifth order. We prove the existence of at least one weak solution as long as the boundary does not touch the axis of symmetry. An explicit expression for a class of divergence-free functions is given.MSC:35Q30, 35Q35, 35D05, 74F10, 76D03.