June  2007, 2(2): 359-381. doi: 10.3934/nhm.2007.2.359

Nonlinear transmission problems for quasilinear diffusion systems

1. 

Dipartimento di Matematica Pura e Applicata, Universitá degli Studi di L'Aquila, Via Vetoio, I–67010 Coppito (L'Aquila), Italy

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  March 2007

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.
Citation: F. R. Guarguaglini, R. Natalini. Nonlinear transmission problems for quasilinear diffusion systems. Networks & Heterogeneous Media, 2007, 2 (2) : 359-381. doi: 10.3934/nhm.2007.2.359
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