Global solutions to a density-suppressed motility system modeling oncolytic virotherapy

We study a partial differential system which is a model of oncolytic virotherapy. It illuminates interaction between infected cancer cells, uninfected cancer cells, extracellular matrix (ECM) and oncolytic viruses. The main result is that the associated initial boundary value problem admits a global classical solution in two-dimensional domains with any given suitably regular initial data, where $\gamma (v) \in C^3([0,\infty ))$, $\gamma (v) \gt 0$, $\gamma^{\prime}(v) \lt 0$ for all $v \geq 0$. By treating $\gamma (v)$ as a weight function and employing the method of weighted energy estimates, we derive the $L^\infty $-bound of $v$ to establish the global existence of classical solutions of the problem with a uniform in time bound.