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

We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…

We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…

This paper studies the dynamical behavior of classical solutions to a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, subject to time-dependent boundary conditions. It is shown that under…

In this paper, we consider $2 \times 2$ hyperbolic systems of conservation laws in one space dimension with characteristic fields satisfying a condition that encompasses genuine nonlinearity and linear degeneracy as well as intermediate…

We consider solutions of two-dimensional $m \times m$ systems hyperbolic conservation laws that are constant in time and along rays starting at the origin. The solutions are assumed to be small $L^\infty$ perturbations of a constant state…

In this paper we consider initial boundary value problem for a parabolic equation with nonlinear memory and absorption under nonlinear nonlocal boundary condition. We prove global existence and blow-up of solutions.

We consider the compressible Navier-Stokes system in three dimensions with general inflow-outflow boundary conditions, meaning that we prescribe a boundary velocity which has non-zero normal component and accordingly the density is…

In this paper, we investigate the initial boundary value problem of the following nonlinear extensible beam equation with nonlinear damping term $$u_{t t}+\Delta^2 u-M\left(\|\nabla u\|^2\right) \Delta u-\Delta u_t+\left|u_t\right|^{r-1}…

This paper studies of a variation of the hyperbolic blow up scenario suggested by Hou and Luo's recent numerical simulation [12]. In particular, we propose a "hyperbolic" surface quasi-geostrophic equation characterized by a incompressible…

This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the…

In this paper, we consider the finite time blow-up results for a parabolic equation coupled with superlinear source term and local linear boundary dissipation. Using a concavity argument, we derive the sufficient conditions for the…

We establish a blowup criterion for the two-dimensional (2D) full compressible Navier-Stokes system. The criterion is given in terms of the divergence of the velocity field only, and is independent of the temperature. It is almost the same…

In this paper we study a two-dimensional chemotaxis-consumption system with singular sensitivity and endowed with Neumann boundary conditions. Sufficient conditions on the data of the problem are given so that the globability of classical…

In this paper, we are concerned with the two-dimensional steady supersonic combustion flows with a contact discontinuity moving through a nozzle of finite length. Mathematically, it can be formulated as a free boundary value problem…

We show the convergence of the zero relaxation limit in systems of $2 \times 2$ hyperbolic conservation laws with stochastic initial data. Precisely, solutions converge to a solution of the local equilibrium approximation as the relaxation…

In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time…

We establish a blow-up criterion in terms of the upper bound of the density and temperature for the strong solution to 2D compressible viscous heat-conductive flows. The initial vacuum is allowed.

We investigate the 2D combustion model with Dirichlet boundary conditions and slip boundary conditions in bounded domains. The global existence of weak and strong solutions and the uniqueness of strong solutions are obtained provided the…

This work is devoted to the study of the initial boundary value problem for a general isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985), which can be used as a phase transition model. We will prove the existence…

We consider nxn hyperbolic systems of balance laws in one-space dimension under the assumption that all negative (resp. positive) characteristics are linearly degenerate. We prove the local exact one-sided boundary null controllability of…