Free boundary problems of Stephan type with prescribed flux

On Free Boundary Problems

Free Boundary Problems

Paradigmatic examples are the classical Stefan problem and more general models of phase transitions, where the free boundary is the moving interface between phases. Other examples come from problems in surface science, plastic molding and glass rolling, filtration through porous media, where free boundaries occur as fronts between saturated and unsaturated regions, and others from reaction-diff...

Random Walks for Solving Boundary-Value Problems with Flux Conditions

We consider boundary-value problems for elliptic equations with constant coefficients and apply Monte Carlo methods to solving these equations. To take into account boundary conditions involving solution’s normal derivative, we apply the new mean-value relation written down at boundary point. This integral relation is exact and provides a possibility to get rid of the bias caused by usually use...

High-Order Finite Element Methods for Moving Boundary Problems with Prescribed Boundary Evolution

We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our approach is the use of a universal mesh: a stationary background mesh containing the domain of interest for all times that adapts to the geometry of the immers...

On similarity solutions for boundary layer flows with prescribed heat flux BERNARD

This paper is concerned with existence, uniqueness and behavior of the solutions of the autonomous third order nonlinear differential equation f ′′′ +(m + 2) f f ′′ −(2m + 1) f ′2 = 0 on R + with the boundary conditions f (0) = −γ, f ′ (∞) = 0 and f ′′ (0) = −1. This problem arises when looking for similarity solutions for boundary layer flows with prescribed heat flux. To study solutions we us...