具有非线性信号产生的拟线性两种群趋化模型解的有界性

Global Boundedness of Solutions in a Quasilinear Two-Species Chemotaxis Model with Nonlinear Signal Secretion

在齐次Neumann边界条件下,主要考虑一类具有非线性信号产生的拟线性两种群趋化模型.在适当的初值假设条件下,当模型中的参数满足一定条件时,研究了该模型解的全局有界性.利用椭圆方程的L^(p)理论、Young不等式、Holder不等式和常微分比较原理等数学工具,当模型中参数在一定的取值范围时,证明该模型存在全局有界经典解.

The paper considers the global boundedness of solutions to a quasilinear two-species chemotaxis model with nonlinear signal production under homogeneous Neumann boundary conditions.When the parameters in the model satisfy certain conditions,the global boundedness of solutions to the model was studied,under appropriate initial assumptions.By using some mathematical tools such as the L^(p) theory of elliptic equations,Young's inequality,Hölder's inequality,and the ODE comparison argument,it is shown that there exist globally bounded classical solutions for the model when the parameters in the model are within a certain range of values.