上海科技大学知识管理系统

["We study a class of reaction-advection-diffusion system","{u(t) = del . (del u - chi del nu/nu u) - u nu + u - u(2+beta )+ B-1, x is an element of Omega, t > 0,","nu(t) = Delta nu - nu + u nu + B-2, x is an element of Omega, t > 0,","for chi > 0 in a smooth bounded domain Omega subset of R-n with n >= 2. In comparison with original urban crime models (Short et al., 2008), the system introduces the logistic source term u - u(2 + beta) to represent the fierce competition among criminals, which helps to reduce difficulties brought by the nonlinear growth term uv and large advection rate. We prove that, for n >= 2, suppose","beta > {0, if n < 4,","n/4 - 1, if n >= 4,","then the classical solutions (u, v) of the above system are uniformly bounded for any chi > 0. Our result expands chi to be arbitrary positive number."]