Existence results for degenerate cross-diffusion systems with application to seawater intrusion

Jana Alkhayal (1) , Régis Monneau (1) , Mustapha Jazar (2) , Samar Issa (2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 Mathematics Department

In this paper, we study degenerate parabolic systems, which are strongly coupled. We prove general existence results, but the uniqueness remains an open question. Our proof of existence is based on a crucial entropy estimate which both control the gradient of the solution and the non-negativity of the solution. Our systems are of porous medium type and our theory applies to models in seawater intrusion both in the confined and unconfined cases.

Domaines: Equations aux dérivées partielles [math.AP]

Jana Alkhayal, Régis Monneau, Mustapha Jazar, Samar Issa. Existence results for degenerate cross-diffusion systems with application to seawater intrusion. 2014. ⟨hal-01038120v1⟩