Differential and Integral Equations

Local classical solutions for a chemical system with free boundary

Stéphane Clain and José-Francisco Rodrigues

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Abstract

This paper treats a two-dimensional, free-boundary problem arising in a mathematical model of chemical attack. A diffusion system is solved with a nonlinear condition on the free boundary, whose velocity is governed by the reaction of the concentrations of several compounds. An existence and uniqueness result of classical solutions is given in Hölder spaces, locally in time, for the corresponding Stefan-like problem to a system of parabolic equations with kinetic boundary condition.

Article information

Source
Differential Integral Equations Volume 13, Number 7-9 (2000), 903-920.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061203

Mathematical Reviews number (MathSciNet)
MR1775239

Zentralblatt MATH identifier
0976.35099

Subjects
Primary: 35R35: Free boundary problems
Secondary: 35K50 35K57: Reaction-diffusion equations

Citation

Clain, Stéphane; Rodrigues, José-Francisco. Local classical solutions for a chemical system with free boundary. Differential Integral Equations 13 (2000), no. 7-9, 903--920. https://projecteuclid.org/euclid.die/1356061203.


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