On the existence of solutions for a parabolic?elliptic chemotaxis model with flux limitation and logistic source

In this article, we study the existence of solutions a parabolic-elliptic system partial differential equations describing behaviour biological species “ u $$ ” and chemical stimulus v in bounded regular domain ? \Omega ? N {\mathbb{R}}&#x0005E;N . The equation for is parabolic with nonlinear second order term chemotaxis type flux limitation as ? ? div ( | ? p 2 ) , -\chi \operatorname{div}\left(u{\left&#x0007C;\nabla v\right&#x0007C;}&#x0005E;{p-2}\nabla v\right), > 1 p>1 substance distribution satisfies elliptic ? + = -\Delta v&#x0002B;v&#x0003D;u. evolution also determined by logistic growth ? \mu u\left(1-u\right) studied under homogeneous Neumann boundary conditions. main result article uniformly < 3 / p<3/2 any ? N\ge