相关论文: Boundary conditions for hyperbolic relaxation syst…
We study the qualitative properties of the unique global viscosity solution of the superquadratic diffusive Hamilton-Jacobi equation with (generalized) homogeneous Dirichlet conditions. We are interested in the phenomena of gradient blow-up…
In this paper we study the hydrodynamic limit of a B.G.K. like kinetic model on domains with boundaries via $BV_{loc}$ theory. We obtain as a consequence existence results for scalar multidimensional conservation laws with kinetic boundary…
This article investigates an energy balance model coupled to the primitive equations by a dynamic boundary condition with and without noise on the boundary. It is shown that this system is globally strongly well-posed both in the…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
We introduce a non-reflecting boundary condition for the simulation of thermal flows with the lattice Boltzmann Method (LBM). We base the derivation on the locally one-dimensional inviscid analysis, and define target macroscopic values at…
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…
In this note we discuss metastability in a long-but-finite range disordered model for the glass transition. We show that relaxation is dominated by configuration belonging to metastable states and associate an in principle computable…
Continuum models are particularly appealing for theoretical studies of bound states, due to simplicity of their bulk Hamiltonians. The main challenge on this path is a systematic description of the boundary, which comes down to determining…
In this work we study constant-coefficient first order systems of partial differential equations and give necessary and sufficient conditions for those systems to have a well posed Cauchy Problem. In many physical applications, due to the…
We consider a class of nonlocal Cahn-Hilliard equations in a bounded domain $\Omega\subset\mathbb{R}^{d}$ $(d\in\{2,3\})$, subject to a nonlocal kinetic rate dependent dynamic boundary condition. This diffuse interface model describes phase…
This paper provides a framework for deriving a new set of necessary conditions for adverse control problems among two players. The distinguish feature of such problems is that the first player has a priori knowledge on the second player…
We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…
A quantum mechanical explanation of the relaxation to equilibrium is shown for macroscopic systems for nonintegrable cases and numerically verified. The macroscopic system is initially in an equilibrium state, subsequently externally…
We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical…
A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially…
We investigate global bounded solutions of higher regularity to boundary value problems for a general linear nonautonomous first order 1D hyperbolic system in a strip. We establish the existence of such solutions under the assumption of…
A boundary control problem for the viscous Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved. Key words: Cahn-Hilliard…
In the present study, a characteristic-based boundary condition scheme is developed for the compressible magnetohydrodynamic (MHD) equations in the general curvilinear coordinate system, which is an extension of the characteristic boundary…
We study two uniform-in-time asymptotic limits for generalized Kuramoto (GK) models. For these GK type models, we first derive the uniform stability estimates with respect to initial data, natural frequency and communication network under a…
In the context of hyperbolic systems of balance laws, the Shizuta-Kawashima coupling condition guarantees that all the variables of the system are dissipative even though the system is not totally dissipative. Hence it plays a crucial role…