JournalsifbVol. 8 , No. 4DOI 10.4171/ifb/151

A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions

  • Fuensanta Andreu

    Universitat de Valencia, Burjassot (Valencia), Spain
  • José M. Mazón

    Universitat de Valencia, Burjassot (Valencia), Spain
  • Julián Toledo

    Universitat de València, Burjassot (Valencia), Spain
  • N. Igbida

    Université de Picardie Jules Verne, Amiens, France
A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions cover

Abstract

In this paper we prove existence and uniqueness of weak solutions for a general degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions. Particular instances of this problem appear in various phenomena with changes of phase like multiphase Stefan problem and in the weak formulation of the mathematical model of the so called Hele Shaw problem. Also, the problem with non-homogeneous Neumann boundary condition is included.