Classical model existence and left resolution

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...

Percolation and the existence of a soft phase in the classical Heisenberg model

We present the results of a numerical investigation of percolation properties in a version of the classical Heisenberg model. In particular we study the percolation properties of the subsets of the lattice corresponding to equatorial strips of the target manifold S2. As shown by us several years ago, this is relevant for the existence of a massless phase of the model. Our investigation yields s...

Proof-terms for classical and intuitionistic resolution

We extend Parigot's-calculus to form a system of realizers for classical logic which reeects the structure of Gentzen's cut-free, multiple-conclusioned, sequent calculus LK when used as a system for proof-search. Speciically, we add (i) a second binding operator, , which realizes classical, multiple-conclusioned disjunction, and (ii) explicit substitutions, , which provide suucient term-structu...

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

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 ...