On some anisotropic reaction-diffusion systems with L1-data modeling the propagation of an epidemic disease Original Research Article

In this paper, we prove the existence of weak solutions for a reaction-diffusion system with general anisotropic diffusivities and transport effects, supplemented with either mixed boundary conditions or no-flux boundary conditions. Initial conditions and external forcing terms are in L1; this does not allow us to use classical variational formulations. Our motivation is a mathematical model describing the spatial propagation in heterogeneous environments of Feline Immunodeficiency Virus, a feline retrovirus.