相关论文: Blow up at the hyperbolic boundary for a 2x2 syste…

In this paper, we develop bound-preserving (BP) finite-volume schemes for hyperbolic conservation laws on adaptive moving meshes. For scalar conservative laws, we rewrite the conventional high-order discretization as a convex combination of…

The hydrodynamic limit of a one dimensional kinetic model describing chemotaxis is investigated. The limit system is a conservation law coupled to an elliptic problem for which the macroscopic velocity is possibly discontinuous. Therefore,…

In this article, we investigate the initial and boundary blow-up problem for the $p$-Laplacian parabolic equation $u_t-\Delta_p u=-b(x,t)f(u)$ over a smooth bounded domain $\Omega$ of $\mathbb{R}^N$ with $N\ge2$, where $\Delta_pu={\rm…

We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. The authors have justified the well-posedness of this problem and have…

We study the inflow-outflow boundary value problem on an interval, the analog of the 1D shock tube problem for gas dynamics, for general systems of hyperbolic-parabolic conservation laws. In a first set of investigations, we study…

This paper proposes a volumetric penalty method to simulate the boundary conditions for a non-linear hyperbolic problem. The boundary conditions are assumed to be maximally strictly dissipative on a non-characteristic boundary. This…

It is an interesting and important topic to study the motion of small particles in a viscous liquid in current applied research. In this paper we assume the particles are convex with arbitrary shapes and mainly investigate the interaction…

Motivated by the initial-boundary value problem for the Einstein equations, we propose a definition of symmetric hyperbolicity for systems of evolution equations that are first order in time but second order in space. This can be used to…

We consider initial boundary-value problems for nonlinear systems of conservation laws in one space variable. It is known that in general different viscous mechanisms yield different solutions in the zero-viscosity limit. Here we focus on…

We introduce a formulation of the initial and boundary value problem for nonlinear hyperbolic conservation laws posed on a differential manifold endowed with a volume form, possibly with a boundary; in particular, this includes the…

We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in…

This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for a rather general attraction-repulsion model, with nonlinear productions, diffusion, sensitivities and logistic term, we detect Lebesgue spaces…

We consider the initial boundary value problem of a pseudo-parabolic equation with singular potential and the exponent $p(x,t)$ depending on both spatial and temporal variables. We prove the finite time blow up and estimate the upper and…

In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of important linear and nonlinear wave equations…

This paper is concerned with the asymptotic stability of the initial-boundary value problem of a singular PDE-ODE hybrid chemotaxis system in the half space $\R_+=[0, \infty)$. We show that when the non-zero flux boundary condition at $x=0$…

We investigate a system related to a particular isothermal gas-solid chromatography process, called ?Pressure Swing Adsorption?, with two species and instantaneous exchange kinetics. This system presents the particularity to have a linearly…

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…

In this paper we consider nonnegative solutions of the following parabolic-elliptic cross-diffusion system \begin{equation*} \left\{ \begin{array}{l} \begin{aligned} &u_t = \Delta u - \nabla(u f(|\nabla v|^2 )\nabla v), \\[6pt] &0= \Delta v…

It is well-known that the Neumann initial-boundary value problem for the minimal-chemotaxis-logistic system in a 2D bounded smooth domain has no blow-up for any choice of parameters. Here, for a large class of kinetic terms including…

This paper is to derive a new blow-up criterion for the 2D full compressible Navier-Stokes equations without heat conduction in terms of the density $\rho$ and the pressure $P$. More precisely, it indicates that in a bounded domain the…