Global existence and uniqueness of solutions for multidimensional weakly parabolic systems arising in chemistry and biology

Pages: 287 - 309, Volume 6, Issue 1, March 2007

doi:10.3934/cpaa.2007.6.287       Abstract        Full Text (239.7K)       Related Articles

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: In this paper we establish general well-posedeness results for a wide class of weakly parabolic $2\times 2$ systems in a bounded domain of $\mathbb R^N$. Our results cover examples arising in sulphation of marbles and chemotaxis, when the density of one chemical component is not diffusing. We show that, under quite general assumptions, uniform $L^\infty$ estimates are sufficient to establish the global existence and stability of solutions, even if in general the nonlinear terms in the equations depend also on the gradient of the solutions. Applications are presented and discussed.

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

Received: March 2006;      Revised: September 2006;      Published: December 2006.