A moving two-reaction zones model: global existence of solutions

On Existence and Nonexistence Global Solutions of Reaction-Diffusion Equations

We consider the initial value problem for the reaction-diffusion equation ut = ∆u + f(u). In this paper we show the existence and nonexistence of the global solutions in time. Especially, we extend the condition of the nonlinear terms to more general. We have the results of the existence and the nonexistence for the equation with the nonlinear term f satisfying lim infs→0 f(s)/sp > 0 and lim su...

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 of Weak Solutions for a Viscous Two-phase Model

The purpose of this paper is to explore a viscous two-phase liquid-gas model relevant for well and pipe flow. Our approach relies on applying suitable modifications of techniques previously used for studying the single-phase isothermal Navier-Stokes equations. A main issue is the introduction of a novel two-phase variant of the potential energy function needed for obtaining fundamental a priori...

Existence of global weak solutions for a phase–field model of a vesicle moving into a viscous incompressible fluid