Global solutions of a doubly tactic resource consumption model with logistic source

We study a doubly tactic resource consumption model bess left{begin{array}{lll} u_t=tr u- ablacd(u abla w),[1mm] v_t=tr v- ablacd(v abla u)+v(1-v^{beta-1}),[1mm] w_t=tr w-(u+v)w-w+r end{array}right. eess in a smooth bounded domain $ooinR^2$ with homogeneous Neumann boundary conditions, where $rin C^1(barOmegatimes[0,infty))cap L^infty(Omegatimes(0,infty))$ is a given nonnegative function fulfilling bess int_t^{t+1}ii| nsqrt{r}|^2<yy for all t>0. eess It is shown that, firstly, if $beta>2$, then the corresponding Neumann initial-boundary problem admits a global bounded classical solution. Secondly, when $beta=2$, the Neumann initial-boundary problem admits a global generalized solution.