Global solutions to a higher-dimensional system related to crime modeling

被引：27

作者：

Freitag, Marcel ^{[1
]}

机构：

[1] Univ Paderborn, Fak Elektrotech Informat & Math, Paderborn, Germany

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 16期

关键词：

local existence; nonexistence; 35A01 existence problems: global existence; 35K55 nonlinear parabolic equations; 35K65 degenerate parabolic equations; PARABOLIC CHEMOTAXIS SYSTEM; SENSITIVITY; EXISTENCE; REPEAT;

D O I：

10.1002/mma.5141

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the system {u(t) = Delta u - chi del . (u/v del v) - uv + B-1 v(t) = Delta v - v + uv + B-2 of partial differential equations for some positive chi and some Omega subset of R-n, n >= 2. While there are results regarding the existence of global solutions in one dimension for any chi > 0, there are not yet any for the higher-dimensional case. This work in which we establish global solutions for any chi is an element of(0, 2/n) is a first step toward filling this gap.

引用

页码：6326 / 6335

页数：10