Nonlinear transmission problems  for quasilinear diffusion systems

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

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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

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.
- nonlinear parabolic equations,
- transmission conditions,
- global existence of solutions,
- porous media,
- sulphation phenomena,
- chemotaxis
Citation: F. R. Guarguaglini, R. Natalini. Nonlinear transmission problems for quasilinear diffusion systems[J]. Networks and Heterogeneous Media, 2007, 2(2): 359-381. doi: 10.3934/nhm.2007.2.359

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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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