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

作者：Bendahmane Mostafa^*; Langlais Michel

来源：Journal of Evolution Equations, 2010, 10(4): 883-904.

DOI：10.1007/s00028-010-0074-y

• S-I-R model
• cross-diffusion system
• weak solutions
• Faedo-Galerkin
• classical solution

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.

• 出版日期2010-11
• 单位INRIA