Global solutions to a chemotaxis

This work is concerned with a chemotaxis-May-Nowak model with superlinear degradation:

$ \begin{eqnarray*} \left\{\begin{array}{lll} u_t = \Delta u-\nabla \cdot(u\nabla v)-u^\kappa-uw+r, \\ v_t = \Delta v-v+uw, \\ w_t = \Delta w-w+v\ \end{array}\right. \end{eqnarray*} $

in a smooth bounded domain $ \Omega\subset \mathbb{R}^2 $ with homogeneous Neumann boundary conditions. It is shown that for arbitrary superlinear degradation rate ($ \kappa>1 $), the problem admits a global generalized solution.