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Strong well‐posedness of a three phase problem with nonlinear transmission condition
Author(s) -
Kotschote Matthias
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1565
Subject(s) - mathematics , uniqueness , nonlinear system , boundary value problem , mathematical analysis , fixed point theorem , contraction mapping , contraction (grammar) , parabolic partial differential equation , transmission (telecommunications) , partial differential equation , physics , medicine , quantum mechanics , electrical engineering , engineering
We prove existence and uniqueness of strong solutions to a quasilinear parabolic‐elliptic system modelling an ionic exchanger. This chemical system consists of three phases connected with nonlinear boundary conditions. The most interesting difficulty of our problem manifests in the nonlinear transmission condition, as almost all quantities are non‐linearly involved in this boundary equation. Our approach is based on the contraction mapping principle, where maximal L p ‐regularity of the associated linear problem is used to obtain a fixed point equation of the starting problem. Copyright © 2012 John Wiley & Sons, Ltd.