Related papers: Global existence and stabilization in a forager-ex…
Assuming that $0<\chi<\sqrt{\frac{2}n}$, $\kappa\ge 0$ and $\mu>\frac{n-2}{n}$, we prove global existence of classical solutions to a chemotaxis system slightly generalizing \[ \begin{split} u_t &= \Delta u - \chi \nabla\cdot ( \frac{u}{v}…
The aim of this note is to present preliminary existence results for a system of cross-diffusion equations defined on a domain with moving boundaries, which model the evolution of the concentrations of different chemical species in a solid…
This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985), which can be used as a phase transition model. We distinguish two cases,…
In this work, we study the global existence of strong solutions and large-time behavior of a two-phase fluid model in a bounded domain. The model consists of the isothermal Euler equations and the isentropic compressible Navier--Stokes…
We consider the homogeneous Landau equation in $\mathbb{R}^3$ with Coulomb potential and initial data in polynomially weighted $L^{3/2}$. We show that there exists a smooth solution that is bounded for all positive times. The proof is based…
We investigate a class of three-component reaction-diffusion systems subject to mass control and a newly introduced structural assumption, referred to as linear intermediate weighted sum condition. Under these hypotheses, we establish the…
This paper is concerned with quasilinear systems of partial differential equations consisting of two hyperbolic operators interacting dissipatively. Its main theorem establishes global-in-time existence and asymptotic stability of strong…
We consider the following fully parabolic Keller--Segel system with logistic source $$ \left\{\begin{array}{ll} u_t=\Delta u-\chi\nabla\cdot(u\nabla v)+ au-\mu u^2,\quad x\in \Omega, t>0, \disp{v_t=\Delta v- v +u},\quad x\in \Omega, t>0,…
We show that a large effective number of commodities can be a source of equilibrium stability and uniqueness: expanding substitution opportunities strengthens aggregate substitution effects. We study finite dated-commodity exchange…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…
This paper is concerned with the global well-posedness of a chemotaxis-Euler system in bounded domains of $\mathbb{R}^2$. Completing the system with physical boundary conditions, we show that the corresponding initial boundary value problem…
We present a new a-priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this…
In the present paper, we investigate both the global exponential stability and the existence of a periodic solution of a general differential equation with unbounded distributed delays. The main stability criterion depends on the dominance…
This paper proves the existence of small-amplitude global-in-time unique mild solutions to both the Landau equation including the Coulomb potential and the Boltzmann equation without angular cutoff. Since the well-known works (Guo, 2002)…
In this work, we investigate a reaction-diffusion system in which both species are influenced by self-diffusion. Due to Hopf's boundary lemma, we obtain the boundedness of the classical solution of the system. By considering a particular…
In this paper we establish a constructive method in order to show global existence and regularity for a class of degenerate parabolic Cauchy problems which satisfy a weak Hoermander condition on a subset of the domain where the data are…
In this paper we consider a model of a nutrient-prey-predator system in a chemostat with general functional responses, using the input concentration of nutrient as the bifurcation parameter. We study the changes in the existence of isolated…
In this paper we investigate a free boundary problem for the diffusive Leslie-Gower prey-predator model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the…
The time-global unique solvability on the reaction diffusion equations for prey-predator models with density-dependent inhibitor and dormancy on predators is established. The crucial step of the proof is to construct time-local non-negative…