We use a geometric approach to prove the existence of smooth travelling wave solutions of
a nonlinear diffusion–reaction equation with logistic kinetics and a convex nonlinear …

In this article, a finite element scheme for a model of the two-species chemotaxis system with
two chemicals is analyzed. Firstly, we suggest a regularized problem of the truncated …

This paper is concerned with the nonlinear stability of traveling wave solutions for a
conserved system of parabolic equations derived from a singular chemotaxis model …

Self-generated gradients have attracted a lot of attention in the recent biological literature. It
is considered as a robust strategy for a group of cells to find its way during a long journey …

In this manuscript, we prove the existence of slow and fast traveling wave solutions in the
original Gatenby–Gawlinski model. We prove the existence of a slow traveling wave solution …

This thesis is concerned with the modeling of collective cell movement and the analysis of
spreading phenomena arising in these models. The starting point of the thesis is the …

Cette thèse s' inscrit dans le domaine de la modélisation du mouvement cellulaire collectif et
de l'analyse de phénomènes de propagation dans ces modèles. Le point de départ de cette …

Reaction-diffusion models with nonlinear diffusion are widely used for studying population
dynamics in biology and ecology. Yet, the relationship between nonlinear diffusion …

This thesis addresses the existence and stability of localised solutions in some nonstandard
systems of partial differential equations. In particular, it locates the linearised spectrum of a …