相关论文: Flux-limited and classical viscosity solutions for…

Our goal in this paper is to prove the global existence of a classical solution for the isentropic nozzle flow. Regarding this problem, there exist some global existence theorems of weak solutions. However, that of classical solutions does…

In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic differential equations. We…

We consider a mean-field control problem with linear dynamics and quadratic control. We apply the vanishing viscosity method: we add a (regularizing) heat diffusion with a small viscosity coefficient and let such coefficient go to zero. The…

This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…

This paper is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in $\R^3$. For less regular data and weaker compatibility condition than those…

The aim of the paper is to construct and justify asymptotic approximations for solutions to quasilinear convection-diffusion problems with a predominance of nonlinear convective flow in a thin cylinder, where an inhomogeneous nonlinear…

We show the existence of Lipschitz-in-space optimal controls for a class of mean-field control problems with dynamics given by a non-local continuity equation. The proof relies on a vanishing viscosity method: we prove the convergence of…

We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…

This paper investigates the optimal control problems for the finite-horizon continuous-time Markov decision processes with delay-dependent control policies. We develop compactification methods in decision processes, and show that the…

Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…

We consider the 3D isentropic compressible Navier-Stokes equations with degenerate viscousities and vacuum. The degenerate viscosities $\mu(\rho)$ and $\lambda(\rho)$ are proportional to some power of density, while the powers of density in…

The 2D Euler system, which governs inviscid incompressible fluid flow, can admit infinitely many steady solutions in a given domain with slip boundary conditions. To select physical classical solutions, we investigate the vanishing…

We consider a class of viscous fluids with a general monotone dependence of the viscous stress on the symmetric velocity gradient. We introduce the concept of dissipative solution to the associated initial boundary value problem inspired by…

Imbert and Monneau proved that Soner's formulation of state constraint problems on a bounded interval is equivalent to the so-called flux-limited formulation they introduced recently. In the multidimensional setting, we show this result for…

We consider an optimal control on networks in the spirit of the works of Achdou et al. (2013) and Imbert et al. (2013). The main new feature is that there are entry (or exit) costs at the edges of the network leading to a possible…

We say that the vanishing viscosity limit holds in the classical sense if the velocity for a solution to the Navier-Stokes equations converges in the energy norm uniformly in time to the velocity for a solution to the Euler equations. We…

We study a generalized vanishing discount problem for Hamilton--Jacobi equations, removing the standard monotonicity assumption, either in a global sense or when integrated against all Mather measures. Specifically, we consider \[ \lambda…

In this paper, we consider the three-dimensional isentropic Navier-Stokes equations for compressible fluids with viscosities depending on density in a power law and allowing initial vacuum. We introduce the notion of regular solutions and…

We consider the two-phase flow model with slip boundary condition in a 3D exterior domains whose boundary is smooth. We establish the global existence of classical solutions of this system provided that the initial energy is suitably small.…

In this article, we study the classical finite-horizon optimal stopping problem for multidimensional diffusions through an approach that differs from what is typically found in the literature. More specifically, we first prove a key…