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March  2007, 6(1): 287-309. doi: 10.3934/cpaa.2007.6.287

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

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), Italy
2. 

Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico 137, I–00161 Rome, Italy

Received  March 2006 Revised  September 2006 Published  December 2006

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: nonlinear parabolic equations, global existence of solutions, Reaction diffusion systems, chemotaxis., porous media, sulphation.
Mathematics Subject Classification: Primary: 65M06; Secondary: 76M20, 76R, 82C4.
Citation: F. R. Guarguaglini, R. Natalini. Global existence and uniqueness of solutions for multidimensional weakly parabolic systems arising in chemistry and biology. Communications on Pure & Applied Analysis, 2007, 6 (1) : 287-309. doi: 10.3934/cpaa.2007.6.287
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