Global existence of solutions to a hyperbolic-parabolic system

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...

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

Global Existence and L∞ Estimates of Solutions for a Quasilinear Parabolic System

ut = ∇ · (|∇u|m∇u) + f(u, v), x ∈ Ω, t > 0, vt = ∇ · (|∇v|n∇v) + g(u, v), x ∈ Ω, t > 0, (1.1) u(x, 0) = u0(x), v(x, 0) = v0(x), x ∈ Ω, u(x, t) = v(x, t) = 0, x ∈ ∂Ω, where Ω is a bounded domain in R(N > 1) with smooth boundary ∂Ω and m,n > 0. For m = n = 0, f(u, v) = uv, g(u, v) = uv and u0(x), v0(x) ≥ 0, the problem (1.1) has been investigated extensively and the existence and nonexistence of ...