Global existence of classical solutions to a combined chemotaxis–haptotaxis model with logistic source

Global existence of classical solutions to a combined chemotaxis–haptotaxis model with logistic source

a r t i c l e i n f o a b s t r a c t This paper deals with a mathematical model of cancer invasion of tissue. The model consists of a system of reaction–diffusion-taxis partial differential equations describing interactions between cancer cells, matrix degrading enzymes, and the host tissue. In two space dimensions, we prove global existence and uniqueness of classical solutions to this model ...

Global Existence of Classical Solutions to a Cancer Invasion Model

This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue. The model consists of three reactiondiffusion-taxis partial differential equations describing interactions between cancer cells, matrix degrading enzymes, and the host tissue. The equation for cell density includes two bounded nonlinear density-dependent chemotactic and haptotactic sensitivity functions. In the ab...

Global Existence of Classical Solutions to a Three-Species Predator-Prey Model with Two Prey-Taxes

Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model.

This paper studies the global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with appropriate initial and mixed boundary conditions. Under some practicable regularity criteria on diffusion item and nonlinearity, we establish the local existence and uniqueness of classical solutions based on a contraction mapping. This local solution can be conti...

Global Existence of Classical Solutions to Shallow Water Equations with Cauchy Data Containing Vacuum

In this paper, we investigate the singularity formulation of Cauchy problem to the viscous compressible rotating shallow water equations. We obtain the global existence of classical solutions with initial vacuum. In particular, the spatial measure of the set of vacuum can be arbitrarily large. 2000 Mathematics Subject Classification: 35Q35; 35M10; 76N10; 76U05.