Autre Publication Scientifique Année : 2023

Regularity results for discontinuous Hamilton-Jacobi equation with a moving in time boundary

Nader El Khatib
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Mamdouh Zaydan
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Résumé

In this paper, we present regularizing effect for continuous and bounded by below viscosity solution u of a Hamitlon-Jacobi equation on a moving in time domain. The boundary is described by a time-dependent function b. For each time t > 0, we consider two different Hamiltonians before and after the junction point b(t) and a flux limited condition at b(t). Our regularizing effect result is established by showing that the solution u satisfies in the viscosity sense ut + b ′ (t)ux ≥-η(t) where η is a locally bounded function. As a consequence, we conclude that u is locally Lipschitz continuous.

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Dates et versions

hal-04393753 , version 1 (15-01-2024)

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  • HAL Id : hal-04393753 , version 1

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Nader El Khatib, Mamdouh Zaydan. Regularity results for discontinuous Hamilton-Jacobi equation with a moving in time boundary. 2023. ⟨hal-04393753⟩
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