相关论文: Viscous Boundary Value Problems for Symmetric Syst…

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…

This paper is devoted to the derivation and mathematical analysis of a wave-structure interaction problem which can be reduced to a transmission problem for a Boussinesq system. Initial boundary value problems and transmission problems in…

The derivation of shallow water models from Navier-Stokes equations is revisited yielding a class of two-layer shallow water models.An improved velocity profile is proposed, based on the superposition of an ideal fluid and a viscous layer…

The viscosity of water induces a vorticity near the free surface boundary. The resulting rotational component of the fluid velocity vector greatly complicates the water wave system. Several approaches to close this system have been…

In this paper, we we study boundary layer problems for the incompressible MHD systems in the presence of physical boundaries with the standard Dirichlet oundary conditions with small generic viscosity and diffusion coefficients. We identify…

In this article we reconsider high Reynolds number boundary layer flows of fluids with viscoelastic properties. We show that a number of previous studies that have attempted to address this problem are, in fact, incomplete. We correctly…

We collect examples of boundary-value problems of Dirichlet and Dirichlet-Neumann type which we found instructive when designing and analysing numerical methods for fully nonlinear elliptic partial differential equations. In particular, our…

We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…

We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…

We consider an isotropic compressible non-dissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid as well as the free…

Mixed boundary value problems for the Navier-Stokes system in a polyhedral domain are considered. Different boundary conditions (in particular, Dirichlet, Neumann, slip conditions) are prescribed on the faces of a polyhedron. The authors…

We consider an initial-boundary value problem for the one-dimensional equations of compressible isentropic viscous and non-resistive magnetohydrodynamic flows. The global well-posedness of strong solutions with general large data is…

We study the nonhomogeneous boundary value problem for Navier-Stokes equations of steady motion of a viscous incompressible fluid in a three-dimensional bounded multiply connected domain. We prove that this problem has a solution in some…

Combining work of Serre and Zumbrun, Benzoni-Gavage, Serre, and Zumbrun, and Texier and Zumbrun, we propose as a mechanism for the onset of cellular instability of viscous shock and detonation waves in a finite-cross-section duct the…

Extending to systems of hyperbolic--parabolic conservation laws results of Howard and Zumbrun for strictly parabolic systems, we show for viscous shock profiles of arbitrary amplitude and type that necessary spectral (Evans function)…

We deal with initial-boundary value problems for systems of conservation laws in one space dimension and we focus on the boundary Riemann problem. It is known that, in general, different viscous approximations provide different limits. In…

Extending investigations of Yarahmadian and Zumbrun in the strictly parabolic case, we study time-asymptotic stability of arbitrary (possibly large) amplitude noncharacteristic boundary layers of a class of hyperbolic-parabolic systems…

We discuss a class of linear control problems in a Hilbert space setting, which covers diverse systems such as hyperbolic and parabolic equations with boundary control and boundary observation even including memory terms. We introduce…

We prove well posedness and stability in $\mathbf{L}^1$ for a class of mixed hyperbolic-parabolic non linear and non local equations in a bounded domain with no flow along the boundary. While the treatment of boundary conditions for the…

We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…