Related papers: Weakly coupled Hamilton-Jacobi systems without mon…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
The purpose of this note is to provide an optimal rate of convergence in the vanishing viscosity regime for first-order Hamilton-Jacobi equations with purely quadratic Hamiltonian. We show that for a globally Lipschitz-continuous terminal…
Main purpose of this paper is to study the local propagation of singularities of viscosity solution to contact type evolutionary Hamilton-Jacobi equation $$ D_tu(t,x)+H(t,x,D_xu(t,x),u(t,x))=0. $$ An important issue of this topic is the…
We consider the diffusive Hamilton-Jacobi equation, with homogeneous Dirichlet conditions and regular initial data. It is known from [Barles-DaLio, 2004] that the problem admits a unique, continuous, global viscosity solution, which extends…
We study the approximation of parabolic Hamilton-Jacobi-Bellman (HJB) equations in bounded domains with strong Dirichlet boundary conditions. We work under the assumption of the existence of a sufficiently regular barrier function for the…
This paper is concerned with a comparison principle for viscosity solutions to Hamilton-Jacobi (HJ), -Bellman (HJB), and -Isaacs (HJI) equations for general classes of partial integro-differential operators. Our approach innovates in three…
This work is devoted to the studies of a Hamilton--Jacobi equation with a quadratic and degenerate Hamiltonian, which comes from the dynamics of a multipeakon in the Camassa--Holm equation. It is given by a quadratic form with a singular…
We investigate the large-time behavior of the value functions of the optimal control problems on the $n$-dimensional torus which appear in the dynamic programming for the system whose states are governed by random changes. From the point of…
We prove the existence of a subsonic weak solution $({\bf u}, \rho, p)$ to steady Euler system in a two-dimensional infinitely long nozzle when prescribing the value of the entropy $(= \frac{p}{\rho^{\gamma}})$ at the entrance by a…
A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower…
The main purpose of this paper is to study the global propagation of singularities of viscosity solution to discounted Hamilton-Jacobi equation \begin{equation}\label{eq:discount 1}\tag{HJ$_\lambda$} \lambda v(x)+H( x, Dv(x) )=0 , \quad…
We study a strongly coupled system consisting of a parabolic equation and a singular Hamilton-Jacobi equation in one space dimension. This system describes the dynamics of dislocation densities in a material submitted to an exterior applied…
In this work we investigate regularity properties of a large class of Hamilton-Jacobi-Bellman (HJB) equations with or without obstacles, which can be stochastically interpreted in form of a stochastic control system which nonlinear cost…
We deal with a weakly coupled system of ODEs of the type $$ x_j'' + n_j^2 \,x_j + h_j(x_1,\ldots,x_d) = p_j(t), \qquad j=1,\ldots,d, $$ with $h_j$ locally Lipschitz continuous and bounded, $p_j$ continuous and $2\pi$-periodic, $n_j \in…
For a class of fully nonlinear equations having second order operators which may be singular or degenerate when the gradient of the solutions vanishes, and having first order terms with power growth, we prove the existence and uniqueness of…
We show strong uniform convergence of monotone P1 finite element methods to the viscosity solution of isotropic parabolic Hamilton-Jacobi-Bellman equations with mixed boundary conditions on unstructured meshes and for possibly degenerate…
We prove the existence and uniqueness of a viscosity solution of the parabolic variational inequality with a nonlinear multivalued Neumann-Dirichlet boundary condition:% {equation*} \{{array}{r} \dfrac{\partial u(t,x)}{\partial…
This paper shows nonlinear stability of homogeneous states in second-order hyperbolic systems of partial differential equations that model the dynamics of dissipative relativistic fluids, by checking a dissipativity criterion formulated…
In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (HJB) equations associated with optimal control problems for path-dependent differential equations. We identify the value…
In this paper, we study a system of second order integro-partial differential equations with interconnected obstacles with non-local terms, related to an optimal switching problem with the jump-diffusion model. Getting rid of the…