A reaction-diffusion system with cross-diffusion modelling the spread of an epidemic disease

Mostafa Bendahmane (1) , Michel Langlais (2, 3)

1 CI²MA - Centro de Investigación en Ingeniería Matemática [Concepción]
2 IMB - Institut de Mathématiques de Bordeaux
3 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics

We provide existence results for nonnegative solutions to a class of reaction-diffusion systems with cross-diffusion modeling the spread of an epidemic disease. The existence of weak solutions is proved by means of an approximation process, the Faedo-Galerkin method, and a compactness argument. Under additional assumptions a global existence result for classical solutions is derived upon using interpolation results between Banach spaces.

Mots clés: S-I-R model; cross-diffusion system; weak solutions; Faedo-Galerkin; classical solution

Domaines: Equations aux dérivées partielles [math.AP]

Mostafa Bendahmane, Michel Langlais. A reaction-diffusion system with cross-diffusion modelling the spread of an epidemic disease. Journal of Evolution Equations, 2010, 10 (4), pp.883-904. ⟨10.1007/s00028-010-0074-y⟩. ⟨hal-00541283⟩