Related papers: Global solution for a kinetic chemotaxis model wit…
In this Series, we study the weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion. In this part, we focus on steady solutions and develop an `adjoint method' for deriving the nonlinear amplitude…
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…
The present work deals with a Keller-Segel-Navier-Stokes system with potential consumption, under homogeneous Neumann boundary conditions for cell density and chemical signal, and of Dirichlet type for the velocity field, over a bounded…
We consider the following chemotaxis systems $$\begin{cases}u_t=\Delta u-\chi_1\nabla(u\nabla v_1)+\chi_2\nabla(u\nabla v_2)+u(a-bu),\ \ x\in\mathbb R^N,t>0,\\0=(\Delta-\lambda_1I)v_1+\mu_1u,\ \ x\in\mathbb…
The study of nonlinear Schr\"odinger-type equations with nonzero boundary conditions define challenging problems both for the continuous (partial differential equation) or the discrete (lattice) counterparts. They are associated with…
This paper is concerned with the development and analysis of a mathematical model that is motivated by interstitial hydrodynamics and tissue deformation mechanics (poro-elasto-hydrodynamics) within an in-vitro solid tumor. The classical…
We show the existence of global-in-time weak solutions to a general class of coupled Hookean-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The…
In this work, we consider a nonlocal Fisher-KPP reaction-diffusion problem with Neumann boundary condition and nonnegative initial data in a bounded domain in $\mathbb{R}^n (n \ge 1)$, with reaction term $u^\alpha(1-m(t))$, where $m(t)$ is…
This article is concerned with the Schauder estimate for linear kinetic Fokker-Planck equations with H\"older continuous coefficients. This equation has an hypoelliptic structure. As an application of this Schauder estimate, we prove the…
We consider an initial-boundary value problem for the incompressible chemotaxis-Navier-Stokes equations generalizing the porous-medium-type diffusion model $ \quad n_t+u\cdot\nabla n=\Delta n^m-\nabla\cdot(n\chi(c)\nabla c), $ $ \quad…
In a previous paper(2021), the author studied the asymptotic behavior of coexistence steady-states to the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. As a result, he proved that…
We introduce the Global Spin Model to study the static and dynamic properties of the ultracold fermionic gas near the broad Feshbach resonance. We show that the problem of molecular production, in a single-mode approximation, is reduced to…
This work concerns the global existence of the weak solutions to a system of partial differential equations modeling the evolution of particles in the fluid. That system is given by a coupling between the standard isentropic compressible…
We consider a nonlinear, strongly coupled, parabolic system arising in the modeling of burglary in residential areas. The system is of chemotaxis-type and involves a logarithmic sensivity function and specific interaction and relaxation…
The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. The equations consist of a reaction-diffusion equation for the substrate concentration and a fourth-order Cahn-Hilliard-type equation…
This paper studies the non-negative solutions of the Keller-Segel model with a nonlocal nonlinear source in a bounded domain. The competition between the aggregation and the nonlocal reaction term is highlighted: when the growth factor is…
We study a phase field model proposed recently in the context of tumour growth. The model couples a Cahn-Hilliard-Brinkman (CHB) system with a elliptic reaction-diffusion equation for a nutrient. The fluid velocity, governed by the Brinkman…
We study the Cauchy problem for the chemotaxis Navier-Stokes equations and the Keller-Segel-Navier-Stokes system. Local-in-time and global-in-time solutions satisfying fundamental properties such as mass conservation and nonnegativity…
We consider the Cauchy problem for 2-D incompressible isotropic elastodynamics. Standard energy methods yield local solutions on a time interval $[0,{T}/{\epsilon}]$, for initial data of the form $\epsilon U_0$, where $T$ depends only on…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…