26 research outputs found
Boundedness in a fully parabolic chemotaxis system with nonlinear diffusion and sensitivity, and logistic source
In this paper we study the zero-flux chemotaxis-system \begin{equation*}
\begin{cases} u_{ t}=\nabla \cdot ((u+1)^{m-1} \nabla u-(u+1)^\alpha
\chi(v)\nabla v) + ku-\mu u^2 & x\in \Omega, t>0, \\ v_{t} = \Delta v-vu & x\in
\Omega, t>0,\\ \end{cases} \end{equation*} being a bounded and smooth
domain of , , and where ,
and . For any the chemotactic sensitivity
function is assumed to behave as the prototype , with and . We prove that for
nonnegative and sufficiently regular initial data and the
corresponding initial-boundary value problem admits a global bounded classical
solution provided is large enough