Related papers: Multiscale Homogenizations for first-order Hamilto…
It was pointed out in [P.L. Lions, G. Papanicolaou, S. Varadhan, Homogenization of Hamilton-Jacobi equation, unpublished preprint (1987)] that, for first order Hamilton-Jacobi (HJ) equations, homogenization starting with affine initial data…
We study the stochastic homogenization for a Cauchy problem for a first-order Hamilton-Jacobi equation whose operator is not coercive w.r.t. the gradient variable. We look at Hamiltonians like $H(x,\sigma(x)p,\omega)$ where $\sigma(x)$ is a…
We investigate the stability with respect to homogenization of classes of integrals arising in the control-theoretic interpretation of some Hamilton-Jacobi equations. The prototypical case is the homogenization of energies with a Lagrangian…
We study the spatial-homogeneity of stable solutions of almost-periodic parabolic equations. It is shown that if the nonlinearity satisfies a concave or convex condition, then any linearly stable almost automorphic solution is…
In the past decade, there are many works on the finite element methods for the fully nonlinear Hamilton--Jacobi--Bellman (HJB) equations with Cordes condition. The linearised systems have large condition numbers, which depend not only on…
In this note we study the convergence of monotone P1 finite element methods on unstructured meshes for fully non-linear Hamilton-Jacobi-Bellman equations arising from stochastic optimal control problems with possibly degenerate, isotropic…
We make use of the Quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasi-solvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasi-solvability of…
The U(1) Calogero-Sutherland Model with anti-periodic boundary condition is studied. This model is obtained by applying a vertical magnetic field perpendicular to the plane of one dimensional ring of particles. The trigonometric form of the…
This paper is concerned with quantitative homogenization of second-order parabolic systems with periodic coefficients varying rapidly in space and time, in different scales. We obtain large-scale interior and boundary Lipschitz estimates as…
We prove, under some assumptions, the existence of correctors for the stochastic homoge-nization of of " viscous " possibly degenerate Hamilton-Jacobi equations in stationary ergodic media. The general claim is that, assuming knowledge of…
We consider boundary value problems for quasilinear first-order one-dimensional hyperbolic systems in a strip. The boundary conditions are supposed to be of a smoothing type, in the sense that the $L^2$-generalized solutions to the…
This paper concerns linear first-order hyperbolic systems in one space dimension of the type $$ \partial_tu_j + a_j(x,t)\partial_xu_j + \sum\limits_{k=1}^nb_{jk}(x,t)u_k = f_j(x,t),\; x \in (0,1),\; j=1,\ldots,n, $$ with periodicity…
We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…
We study the homogenization of a Hamilton-Jacobi equation forced by rapidly oscillating noise that is colored in space and white in time. It is shown that the homogenized equation is deterministic, and, in general, the noise has an…
In this paper, we show that the concept of sigma-convergence associated to stochastic processes can tackle the homogenization of stochastic partial differential equations. In this regard, the homogenization problem for a stochastic…
In this paper we study the convergence of monotone $P1$ finite element methods for fully nonlinear Hamilton-Jacobi-Bellman equations with degenerate, isotropic diffusions. The main result is strong convergence of the numerical solutions in…
This paper addresses the issue of homogenization of linear divergence form parabolic operators in situations where no ergodicity and no scale separation in time or space are available. Namely, we consider divergence form linear parabolic…
We address the problem of combined stochastic and impulse control for a market maker operating in a limit order book. The problem is formulated as a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). We propose an implicit…
In this paper, for a family of second-order elliptic equations with rapidly oscillating periodic coefficients, we are interested in a Carleman-type inequality for these solutions satisfying an additional growth condition in elliptic…
In this paper a second-order homogenization approach for periodic material is derived from an appropriate representation of the down-scaling that correlates the microdisplacement field to the macro-displacement field and the macro-strain…