Beckmann-type problem for degenerate Hamilton-Jacobi equations

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2021-12-21 DOI:10.1090/qam/1606

Hamza Ennaji, N. Igbida, Van Thanh Nguyen

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引用次数: 5

Abstract

The aim of this note is to give a Beckmann-type problem as well as the corresponding optimal mass transportation problem associated with a degenerate Hamilton-Jacobi equation H ( x , ∇ u ) = 0 , H(x,\nabla u)=0, coupled with non-zero Dirichlet condition u = g u=g on ∂ Ω \partial \Omega . In this article, the Hamiltonian H H is continuous in both arguments, coercive and convex in the second, but not enjoying any property of existence of a smooth strict sub-solution. We also provide numerical examples to validate the correctness of theoretical formulations.

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退化Hamilton-Jacobi方程的Beckmann型问题

本文的目的是给出一个beckmann型问题以及与简并Hamilton-Jacobi方程H(x，∇u)=0, H(x, \nabla u)=0，以及∂Ω \partial\Omega上的非零Dirichlet条件u=g u=g相关的相应的最优质量输运问题。在本文中，哈密顿矩阵H H在两个论证中都是连续的，在第二个论证中是强制的和凸的，但不具有光滑严格子解存在的性质。通过数值算例验证了理论公式的正确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.