相关论文: Global existence for the kinetic chemotaxis model …
In this paper we consider kinetic and associated macroscopic models for chemotaxis on a network. Coupling conditions at the nodes of the network for the kinetic problem are presented and used to derive coupling conditions for the…
In this paper, we prove the existence and uniqueness of the global solution to the reaction diffusion system SKT with homogeneous Newmann boundary conditions. We use the lower and upper solution method and its associated monotone iterations…
Biopolymer length regulation is a complex process that involves a large number of subprocesses acting simultaneously across multiple spatial and temporal scales. An illustrative example important for genomic stability is the length…
Surface growth, by association or dissociation of material on the boundaries of a body, is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a…
The aim of this work is to study the global existence of solutions for some coupled systems of reaction diffusion which describe the spread within a population of infectious disease. We consider a triangular matrix diffusion and we show…
To describe the cellular self-aggregation phenomenon, some strongly coupled PDEs named as Keller-Segel (KS) and Patlak-Keller-Segel (PKS) systems were proposed in 1970s. Since KS and PKS systems possess relatively simple structures but…
Bacterial chemotaxis is one of the most extensively studied adaptive responses in cells. Many bacteria are able to bias their apparently random motion to produce a drift in the direction of the increasing chemoattractant concentration. It…
We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent $0<\alpha\leq 2$. We prove some features related to the classical two-dimensional…
We construct the kinetic theory in ($1+2d$)-dimensional phase space and time when all abelian and nonabelian phase-space Berry curvatures are nonzero. Then we calculate anomalous transports induced by the Berry curvatures on the basis of…
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear differential equations assuming a very general form of dichotomic behavior for the linear equation. Besides some new…
Navigation of microorganisms is controlled by internal processes ultimately sensitive to mechanical or chemical signaling encountered along the path. In many natural environments, such as porous soils or physiological ducts, motile species…
Exchange-driven growth is a process in which pairs of clusters interact and exchange a single unit of mass. The rate of exchange is given by an interaction kernel $K(j,k)$ which depends on the masses of the two interacting clusters. In this…
Active matter comprises individual units that convert energy into mechanical motion. In many examples, such as bacterial systems and biofilament assays, constituent units are elongated and can give rise to local nematic orientational order.…
Run-and-tumble is a basic model of persistent motion and a motility strategy widespread in micro-organisms and individual cells. In many natural settings, movement occurs in the presence of confinement. While accumulation at the surface has…
We consider a partial differential equation that arises in the coarse-grained description of epitaxial growth processes. This is a parabolic equation whose evolution is governed by the competition between the determinant of the Hessian…
In this paper, we derive a new chemotaxis model with degenerate diffusion and density-dependent chemotactic sensitivity, and we provide a more realistic description of cell migration process for its early and late stages. Different from the…
We have developed a two dimensional stochastic molecular dynamics model for the description of intra cellular collective motion of bio motors, in particular Kinesins, on a microtubular track. The model is capable or reproducing the…
In this paper we propose a numerical study of macroscopic models for collective cell migration, focusing on a multi-dimensional pressureless Euler-type model with non-local interactions coupled with chemotaxis, rigorously derived from…
We provide a proof of global regularity of solutions of some models of viscoelastic flow with an integral constitutive law, in the two spatial dimensions and in a periodic domain. Models that are included in these results are classical…
In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic…