Networks and Heterogeneous Media (NHM)

Nonlinear transmission problems for quasilinear diffusion systems

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

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

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.

Keywords:  nonlinear parabolic equations, transmission conditions, global existence of solutions, porous media, sulphation phenomena, chemotaxis
Mathematics Subject Classification:  Primary 65M06; Secondary 76M20, 76R, 82C40.

Received: January 2007;      Revised: March 2007;      Available Online: March 2007.