45 citations · 211 across the 47 of their papers we have counts for
7 papers · 2 filters
Incompressible limit of mechanical model of tumor growth with viscosity
Benoit Perthame, Nicolas Vauchelet
Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic mate…
The Filippov characteristic flow for the aggregation equation with mildly singular potentials
José Antonio Carrillo, Francois James, Frédéric Lagoutière +1
Existence and uniqueness of global in time measure solution for the multidimensional aggregation equation is analyzed. Such a system can be written as a continuity equation with a…
Existence and diffusive limit of a two-species kinetic model of chemotaxis
Luís Almeida, Casimir Emako, Nicolas Vauchelet
In this paper, we propose a kinetic model describing the collective motion by chemotaxis of two species in interaction emitting the same chemoattractant. Such model can be seen as…
Numerical methods for one-dimensional aggregation equations
Francois James, Nicolas Vauchelet
We focus in this work on the numerical discretization of the one dimensional aggregation equation $\pa_tρ+ \pa_x (vρ)=0$, , in the attractive case. Finite time blow up o…
Transversal instability for the thermodiffusive reaction-diffusion system
Michal Kolwalczyk, Benoit Perthame, Nicolas Vauchelet
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bac…
Traveling wave solution of the Hele-Shaw model of tumor growth with nutrient
Benoît Perthame, Min Tang, Nicolas Vauchelet
Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical…