Generalized Solutions to Semilinear Hyperbolic Systems.
In this paper several models in virus dynamics with and without immune response are discussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses and T-cells is included. It is shown that, depending on the value of the basic reproductive number R0 of the virus, the corresponding equilibrium is globally asymptotically stable. If R0 < 1 then the virus-free equilibrium has this property, and in case R0 > 1 there is a unique disease equilibrium which takes over this...
The Fujita type global existence and blow-up theorems are proved for a reaction-diffusion system of m equations (m>1) in the form