Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system

On the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis

We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller–Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

A Quasi-linear Parabolic System of Chemotaxis

We consider a quasi-linear parabolic system with respect to unknown functions u and v on a bounded domain of n-dimensional Euclidean space. We assume that the diffusion coefficient of u is a positive smooth function A(u), and that the diffusion coefficient of v is a positive constant. If A(u) is a positive constant, the system is referred to as socalled Keller-Segel system. In the case where th...

A priori bounds and global existence for a strongly coupled quasilinear parabolic system modeling chemotaxis

A priori bounds are found for solutions to a strongly coupled reactiondiffusion system that models competition of species in the presence of chemotaxis. These bounds are used to prove the existence of global solutions.

The Dirichlet Problem for Quasilinear Elliptic and Parabolic Equations

We prove comparison results between continuous and dis-continuous viscosity sub-and super-solutions of the generalized Dirichlet problem for quasilinear elliptic and parabolic equations. The main consequence of these results is the uniqueness of continuous solutions of such problems, when they exist.