We study a parabolic–parabolic chemotactic PDE’s system which describes the evolution of a biological population “u” and a chemical substance “v” in a two-dimensional bounded domain with regular boundary. We consider a growth term of logistic type in the equation of “u” in the form \(u (1-u+f(x,t))\), for a given bounded function “f” which tends to a periodic in time function independent of x when t goes to infinity. We study the global existence of solutions and its asymptotic behavior for a range of parameters and initial data.

中文翻译：

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具有源项和周期渐近行为的全抛物趋化系统

我们研究了抛物线-抛物线趋化PDE系统，该系统描述了具有规则边界的二维有界域中生物种群“ u ”和化学物质“ v ”的演化。对于给定的有界函数“ f ”，我们在方程“ u ”中以\（u（1-u + f（x，t））\）的形式考虑逻辑类型的增长项。当t变为无穷大时，时间函数与x无关。我们研究了一系列参数和初始数据的整体存在性及其解的渐近行为。