Zobrazeno 1 - 10
of 575
pro vyhledávání: '"Perthame, Benoît"'
Publikováno v:
Comptes Rendus. Mécanique, Vol , Iss , Pp 1-20 (2023)
The Cahn–Hilliard equation with degenerate mobility is used in several areas including the modeling of living tissues, following the theory of mixtures. We are interested in quantifying the pressure jump at the interface between phases in the case
Externí odkaz:
https://doaj.org/article/edb80b4e2fe04df6be427b9ddf4ce66e
The integrate and fire equation is a classical model for neural assemblies which can exhibit finite time blow-up. A major open problem is to understand how to continue solutions after blow-up. Here we study an approach based on random discharge model
Externí odkaz:
http://arxiv.org/abs/2409.14749
One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production of matrix m
Externí odkaz:
http://arxiv.org/abs/2404.05730
Autor:
Loy, Nadia, Perthame, Benoit
Highly concentrated patterns have been observed in a spatially heterogeneous, nonlocal, model of BGK type implementing a velocity-jump process. We study both a linear and a nonlinear case and describe the concentration profile. In particular, we anal
Externí odkaz:
http://arxiv.org/abs/2401.17176
The motile micro-organisms such as E. coli, sperm, or some seaweed are usually modelled by self-propelled particles that move with the run-and-tumble process. Individual-based stochastic models are usually employed to model the aggregation phenomenon
Externí odkaz:
http://arxiv.org/abs/2401.03161
We revisit the problem of proving the incompressible limit for the compressible porous media equation with Newtonian drift and growth. The question is motivated by models of living tissues development including chemotaxis. We extend the problem, alre
Externí odkaz:
http://arxiv.org/abs/2312.16869
Neuron models have attracted a lot of attention recently, both in mathematics and neuroscience. We are interested in studying long-time and large-population emerging properties in a simplified toy model. From a mathematical perspective, this amounts
Externí odkaz:
http://arxiv.org/abs/2307.13362
The non-local degenerate Cahn-Hilliard equation is derived from the Vlasov equation with long-range attraction. We study the local limit as the delocalization parameter converges to 0. The difficulty arises from the degeneracy which requires compactn
Externí odkaz:
http://arxiv.org/abs/2306.06486
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations with a no
Externí odkaz:
http://arxiv.org/abs/2306.01777
The link between compressible models of tissue growth and the Hele-Shaw free boundary problem of fluid mechanics has recently attracted a lot of attention. In most of these models, only repulsive forces and advection terms are taken into account. In
Externí odkaz:
http://arxiv.org/abs/2305.06239