Related papers: Singular convergence of nonlinear hyperbolic chemo…
This paper studies the quantitative unique continuation for a semi-linear parabolic-elliptic coupled system on a bounded domain. This system is a simplified version of the chemotaxis model introduced by Keller and Segel. With the aid of…
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…
The focus of this paper is on solutions to a two-dimensional Keller-Segel system containing sub-logistic sources. We show that the presence of sub-logistic terms is adequate to prevent blow-up phenomena even in strongly degenerate…
The parabolic-elliptic cross-diffusion system \[ \left\{ \begin{array}{l} u_t = \Delta u - \nabla \cdot \Big(uf(|\nabla v|^2) \nabla v \Big), \\[1mm] 0 = \Delta v - \mu + u, \qquad \int_\Omega v=0, \qquad \mu:=\frac{1}{|\Omega|} \int_\Omega…
It is shown in \cite[J. Differ. Equ., (2022)]{22jde} that given initial data $u_0\in B^{s}_{p,r}$ and for some $T>0$, the solutions of the parabolic-type Keller-Segel equations converge strongly in $L^\infty_TB^{s}_{p,r}$ to the hyperbolic…
The purpose of this work is the study of \textit{chemotaxis} and how to model it through the equations of Keller-Segel. \textit{Chemotaxis} is a natural process which induces the organisms to direct their movement according to certain…
This paper is concerned with the density-suppressed motility model: $u_{t}=\Delta (\displaystyle\frac{u^m}{v^\alpha}) +\beta uf(w), v_{t}=D\Delta v-v+u, w_{t}=\Delta w-uf(w)$ in a smoothly bounded convex domain $\Omega\subset…
Numerous evolution equations with nonlocal convolution-type interactions have been proposed. In some cases, a convolution was imposed as the velocity in the advection term. Motivated by analyzing these equations, we approximate advective…
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the…
This work concerns the numerical approximation with a finite volume method of inviscid, nonequilibrium, high-temperature flows in multiple space dimensions. It is devoted to the analysis of the numerical scheme for the approximation of the…
We study the blow-up asymptotics of radially decreasing solutions of the parabolic-elliptic Keller-Segel-Patlak system in space dimensions $n\ge 3$. In view of the biological background of this system and of its mass conservation property,…
In this paper we study the effect of the addition of a convective term, and of the resulting increased dissipation rate, on the growth of solutions to a general class of non-linear parabolic PDEs. In particular, we show that blow-up in…
In this paper we investigate the one-dimensional parabolic-parabolic Patlak-Keller-Segel model of chemotaxis. For the case when the diffusion coefficient of chemical substance is equal to two, in terms of travelling wave variables the…
This paper is concerned with the global boundedness and blowup of solutions to the Keller-Segel system with density-dependent motility in a two-dimensional bounded smooth domain with Neumman boundary conditions. We show that if the motility…
We consider a Keller-Segel model with non-linear porous medium type diffusion and non-local attractive power law interaction, focusing on potentials that are less singular than Newtonian interaction. Here, the nonlinear diffusion is chosen…
The phenomenon where cells with elongated protrusions, such as neurons, communicate by contacting other cells and arrange themselves appropriately is termed cell sorting through haptotaxis. This phenomenon is described by partial…
This paper presents a study of nonlinear superpositions of Riemann wave solutions admitted by quasilinear hyperbolic first-order systems of partial differential equations. In particular, we focus on the Euler system and non-elastic wave…
We investigate a class of Vlasov-type kinetic flocking models featuring nonlinear velocity alignment. Our primary objective is to rigorously derive the hydrodynamic limit leading to the compressible Euler system with nonlinear alignment.…
In this paper, we investigate the long-time dynamics of a repulsive Keller-Segel chemotaxis system. The model features negative chemotaxis, logistic growth and a cell death term, accounting for a lethal chemorepellent that is self-produced…
We consider a parabolic-parabolic Keller-Segel system of chemotaxis model with singular sensitivity $u_t=\Delta u-\chi\nabla\cdot(\frac{u}{v}\nabla v)$, $v_t=k\Delta v-v+u$ under homogeneous Neumann boundary conditions in a smooth bounded…