A PDE Approach to the Long-Time Asymptotic Solutions of Contact Hamilton-Jacobi Equations

Yujie Wang,Xia Li

doi:10.1051/wujns/2022273189

A PDE Approach to the Long-Time Asymptotic Solutions of Contact Hamilton-Jacobi Equations

Yujie Wang, Xia Li

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https://doi.org/10.1051/wujns/2022273189

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Journal: Wuhan University Journal of Natural Sciences	Publication Date: Jun 1, 2022
License type: CC BY 4.0

Affiliation: Suzhou University of Science and Technology

#Formula In PDF #Viscosity Solution Of Hamilton-Jacobi Equation + Show 8 more

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Abstract

We study the long-time asymptotic behaviour of viscosity solutions [see formula in PDF] of the Hamilton-Jacobi equation [see formula in PDF] in [see formula in PDF] with a PDE approach, where [see formula in PDF] is coercive in [see formula in PDF], non-decreasing in [see formula in PDF] and strictly convex in [see formula in PDF], and establish the uniform convergence of [see formula in PDF] to an asymptotic solution [see formula in PDF] as [see formula in PDF]. Moreover, [see formula in PDF] is a viscosity solution of Hamilton-Jacobi equation [see formula in PDF].

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