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2007, Volume 2, Issue 2: 359-381. Doi: 10.3934/nhm.2007.2.359

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Nonlinear transmission problems for quasilinear diffusion systems

F. R. Guarguaglini^1, and
R. Natalini^2,

1.
Dipartimento di Matematica Pura e Applicata, Universitá degli Studi di L'Aquila, Via Vetoio, I–67010 Coppito (L'Aquila)
2.
Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico 137, I–00161 Rome

Received: January 2007

Revised: March 2007

Published: June 2007

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Abstract

We study degenerate quasilinear parabolic systems in two different domains, which are connected by a nonlinear transmission condition at their interface. For a large class of models, including those modeling pollution aggression on stones and chemotactic movements of bacteria, we prove global existence, uniqueness and stability of the solutions.

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Mathematics Subject Classification: Primary 65M06; Secondary 76M20, 76R, 82C40.

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