L1‐type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton‐Jacobi equations
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DOI: 10.1002/fld.4855
Abstract: This article presents an improved fifth‐order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton‐Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local… read more here.
Keywords: essentially nonoscillatory; jacobi equations; weighted essentially; hamilton jacobi ... See more keywords
Dimension-by-dimension moment-based central Hermite WENO schemes for directly solving Hamilton-Jacobi equations
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DOI: 10.1007/s10444-017-9515-2
Abstract: In this paper, a class of high-order central Hermite WENO (HWENO) schemes based on finite volume framework and staggered meshes is proposed for directly solving one- and two-dimensional Hamilton-Jacobi (HJ) equations. The methods involve the… read more here.
Keywords: dimension; central hermite; hermite weno; jacobi equations ... See more keywords
Algorithm for Overcoming the Curse of Dimensionality For Time-Dependent Non-convex Hamilton–Jacobi Equations Arising From Optimal Control and Differential Games Problems
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DOI: 10.1007/s10915-017-0436-5
Abstract: In this paper we develop a parallel method for solving possibly non-convex time-dependent Hamilton–Jacobi equations arising from optimal control and differential game problems. The subproblems are independent so they can be implemented in an embarrassingly… read more here.
Keywords: curse dimensionality; control; time; jacobi equations ... See more keywords
An Alternative Formulation of Discontinous Galerkin Schemes for Solving Hamilton–Jacobi Equations
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DOI: 10.1007/s10915-018-0794-7
Abstract: The aim of this paper is to develop an alternative formulation of discontinuous Galerkin (DG) schemes for approximating the viscosity solutions to nonlinear Hamilton–Jacobi (HJ) equations. The main difficulty in designing DG schemes lies in… read more here.
Keywords: jacobi equations; galerkin schemes; alternative formulation; hamilton jacobi ... See more keywords
Exponential convergence of solutions for random Hamilton–Jacobi equations
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DOI: 10.1007/s40072-019-00153-7
Abstract: We show that for a family of randomly kicked Hamiton-Jacobi equations on the torus, almost surely, the solution of an initial value problem converges exponentially fast to the unique stationary solution. Combined with the results… read more here.
Keywords: solutions random; convergence solutions; exponential convergence; jacobi equations ... See more keywords
Lasry–Lions approximations for discounted Hamilton–Jacobi equations
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DOI: 10.1016/j.jde.2018.03.010
Abstract: We study the Lasry-Lions approximation using the kernel determined by the fundamental solution with respect to a time-dependent Tonelli Lagrangian. This approximation process is also applied to the viscosity solutions of the discounted Hamilton-Jacobi equations. read more here.
Keywords: jacobi equations; discounted hamilton; hamilton jacobi; lasry lions ... See more keywords
An asymptotic analysis for Hamilton–Jacobi equations with large Hamiltonian drift terms
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DOI: 10.1515/acv-2017-0046
Abstract: Abstract We investigate the asymptotic behavior of solutions of Hamilton–Jacobi equations with large Hamiltonian drift terms in an open subset of the two-dimensional Euclidean space. The drift is given by ε-1(Hx2,-Hx1){{\varepsilon}^{-1}(H_{x_{2}},-H_{x_{1}})} of a Hamiltonian H,… read more here.
Keywords: large hamiltonian; hamiltonian drift; jacobi equations; equations large ... See more keywords