Global existence and uniform boundedness of smooth solutions to a parabolic-parabolic chemotaxis system with nonlinear diffusion

Global existence of solutions to a parabolic-elliptic chemotaxis system with critical degenerate di ffusion

Global Existence of Solutions to a Hyperbolic-parabolic System

In this paper, we investigate the global existence of solutions to a hyperbolic-parabolic model of chemotaxis arising in the theory of reinforced random walks. To get L2-estimates of solutions, we construct a nonnegative convex entropy of the corresponding hyperbolic system. The higher energy estimates are obtained by the energy method and a priori assumptions.

Global Solutions for a Hyperbolic-parabolic System of Chemotaxis

We study a hyperbolic-parabolic model of chemotaxis in dimensions one and two. In particular, we prove the global existence of classical solutions in certain dissipation regimes.

Global existence of solutions to a singular parabolic/Hamilton-Jacobi coupled system with Dirichlet conditions

We study the existence of (distribution/viscosity) solutions of a singular parabolic/Hamilton-Jacobi coupled system. Our motivation stems from the study of the dynamics of dislocation densities in a crystal of finite size. The method of the proof consists in considering a parabolic regularization of the system, and then passing to the limit after obtaining some uniform bounds using in particula...

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.