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Singular elliptic and parabolic problems and a class of free boundary problems
Author(s) -
Guidotti Patrick
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700658
Subject(s) - class (philosophy) , free boundary problem , boundary value problem , mathematics , boundary (topology) , mathematical analysis , singular solution , diffusion , elliptic boundary value problem , physics , computer science , thermodynamics , artificial intelligence
In this short contribution we report on some recently made progress in the analytical treatment of a class of Free Boundary Problems (FBPs) characterized by the initial onset of a phase. The analysis is motivated by a model problem arising in the description of case II diffusion in polymers. The main local well‐posedness and regularity theorem is obtained by means of fundamental results concerning the underlying singular elliptic and parabolic boundary value problems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)