Related papers: On C^0-variational solutions for Hamilton-Jacobi e…
We consider a path-dependent Hamilton--Jacobi equation with coinvariant derivatives over the space of continuous functions. We prove two uniqueness results for viscosity (generalized) solutions defined in terms of coinvariantly smooth test…
Motivated by parallels between mean field games and random matrix theory, we develop stochastic optimal control problems and viscosity solutions to Hamilton-Jacobi equations in the setting of non-commutative variables. Rather than real…
This work is devoted to the analysis of the backward problem for a viscous Hamilton-Jacobi equation with degenerate diffusion and a general Hamiltonian that is not necessarily quadratic. First, we focus on linear degenerate parabolic…
The paper deals with a zero-sum differential game for a dynamical system which motion is described by a nonlinear delay differential equation under an initial condition defined by a piecewise continuous function. The corresponding Cauchy…
In this paper, we study evolutive Hamilton Jacobi equations with Hamiltonians that are discontinuous in time, posed on a simple network consisting of two edges on the real line connected at a single junction. We introduce a notion of…
We consider a sequence of finite irreducible Markov chains with exponentially small transition rates: the transition graph is a fixed, finite, strongly connected directed graph; the transition rates decay exponentially on a paramenter N…
Extending the approach of Grillakis-Shatah-Strauss, Bronski-Johnson-Kapitula, and others for Hamiltonian systems, we explore relations between the constrained variational problem $\min_{X:C(X)=c_0} \mathcal{E}(X)$, $c_0\in \RM^r$, and…
The large time behavior of solutions to Cauchy problem for viscous Hamilton-Jacobi equation is classified. The large time asymptotics are given by very singular self-similar solutions on one hand and by self-similar viscosity solutions on…
In this article, we are interested in the large time behavior of solutions of the Dirichlet problem for subquadratic viscous Hamilton-Jacobi Equations. In the superquadratic case, the third author has proved that these solutions can have…
The algebraic-geometric approach is extended to study solutions of N-component systems associated with the energy dependent Schrodinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows…
The author presented a stochastic and variational approach to the Lax-Friedrichs finite difference scheme applied to hyperbolic scalar conservation laws and the corresponding Hamilton-Jacobi equations with convex and superlinear…
In this work, we characterize the solution of a system of elliptic integro-differential equations describing a phenotypically structured population subject to mutation, selection and migration between two habitats. Assuming that the effects…
The paper deals with a Bolza optimal control problem for a dynamical system which motion is described by a delay differential equation under an initial condition defined by a piecewise continuous function. For the value functional in this…
We consider Hamiltonians associated to optimal control problems for affine systems on the torus. They are not coercive and are possibly unbounded from below in the direction of the drift of the system. The main assumption is the strong…
We consider viscosity solutions of Hamilton-Jacobi equations with oscillatory spatial dependence and rough time dependence. The time dependence is in the form of the derivative of a continuous path that converges to a possibly…
Viscosity solutions of fully nonlinear, local or non local, Hamilton-Jacobi equations with a super-quadratic growth in the gradient variable are proved to be H\"older continuous, with a modulus depending only on the growth of the…
We prove that the solution of the discounted approximation of a degenerate viscous Hamilton--Jacobi equation with convex Hamiltonians converges to that of the associated ergodic problem. We characterize the limit in terms of stochastic…
We prove that the multi-time Hamilton-Jacobi equation in general cannot be solved in the viscosity sense, in the non-convex setting, even when the Hamiltonians are in involution.
This paper deals with the periodic homogenization of nonlocal parabolic Hamilton-Jacobi equations with superlinear growth in the gradient terms. We show that the problem presents different features depending on the order of the nonlocal…
We consider a stochastic model for the evolution of a discrete population structured by a trait with values on a finite grid of the torus, and with mutation and selection. Traits are vertically inherited unless a mutation occurs, and…