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Time global existence and asymptotic behavior of solutions to degenerate quasi-linear parabolic systems of chemotaxis
The following degenerate parabolic system modelling chemotaxis is considered. $$ {\mbox{(KS)}} \qquad\qquad \left\{ \begin{array}{llll} & u_t = \nabla \cdot \Big( \nabla u^m - u \nabla v \Big), & x \in \mathbb R^N, \ 0 <t <T, \nonumber \\ & \tau v_t = \Delta v - v + u, & x …