一类具有物流源的双策略资源消耗模型的全局解
Global solutions of a doubly tactic resource consumption model with logistic source
摘要：
研究了一个双策略资源消耗模型\bess \left\{\begin{array}{lll} u_t=\tr u-\nabla\cd(u\nabla w),\\[1mm] v_t=\tr v-\nabla\cd(v\nabla u)+v(1-v^{β-1}),\\[1mm] w_t=\tr w-(u+v)w-w+r \end{array} \right.具有齐次Neumann边界条件的光滑有界域$\oo\in\R^2$中的\eess，其中$r\in C^1(\barΩ\times[0,\infty))\cap L^\infty(Ω\times(0,\infty))$是满足\bess \int_t^{t+1} \ii的给定非负函数|\nn \sqrt{r}| ^2 <\yy\\for\all\t> 0。\eess证明了：（1）若$β>2$，则相应的Neumann初边值问题存在整体有界经典解.其次，当$β=2$时，Neumann初边值问题存在整体广义解。
英文摘要：
We study a doubly tactic resource consumption model \bess \left\{\begin{array}{lll} u_t=\tr u-\nabla\cd(u\nabla w),\\[1mm] v_t=\tr v-\nabla\cd(v\nabla u)+v(1-v^{β-1}),\\[1mm] w_t=\tr w-(u+v)w-w+r \end{array}\right. \eess in a smooth bounded domain $\oo\in\R^2$ with homogeneous Neumann boundary conditions, where $r\in C^1(\barΩ\times[0,\infty))\cap L^\infty(Ω\times(0,\infty))$ is a given nonnegative function fulfilling \bess \int_t^{t+1}\ii|\nn\sqrt{r}|^2<\yy\ \ \ \ \ \ for\ all\ t>0. \eess It is shown that, firstly, if $β>2$, then the corresponding Neumann initial-boundary problem admits a global bounded classical solution. Secondly, when $β=2$, the Neumann initial-boundary problem admits a global generalized solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
