| Abstract: |
| In this talk, we consider a three-component reaction-diffusion system, originating from the classical May-Nowak model for viral infections with superlinear dampening $-\mu u^{\alpha}$. Existence of classical solutions is verified and large time behavior of the solutions are investigated under the condition $\alpha>\frac{n+2}{2}$, while generalized solutions are constructed for arbitrary $\alpha>1$. In addition, based on an analysis of a certain eventual Lyapunov-type functional, we prove that whenever $\alpha>\max\{1,\frac{n}{2}\}$, the corresponding generalized solution asymptotically enjoys relaxation by approaching the nontrivial homogeneous steady states. |
|