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- W3100836443 abstract "We present qualitative and quantitative homogenization results for pathwise Hamilton–Jacobi equations with “rough” multiplicative driving signals. When there is only one such signal and the Hamiltonian is convex, we show that the equation, as well as equations with smooth approximating paths, homogenize. In the multi-signal setting, we demonstrate that blow-up or homogenization may take place. The paper also includes a new well-posedness result, which gives explicit estimates for the continuity of the solution map and the equicontinuity of solutions in the spatial variable. Nous présentons des résultats qualitatifs et quantitatifs d'homogénéisation pour des équations de Hamilton–Jacobi avec des termes de forçage multiplicatifs irréguliers. Dans le cas d'un seul forçage et d'un Hamiltonien convexe, nous montrons que l'équation elle-même, et les équations qui l'approchent pour des forçages réguliers, s'homogénéisent. Dans le cas de plusieurs forçages, nous prouvons que l'explosion ou l'homogénéisation sont possibles. L'article contient aussi un nouveau résultat sur le caractère bien posé de l'équation, qui donne des estimées explicites sur la continuité de l'application qui aux termes de forçages et à la condition initiale associe la solution, ainsi que sur l'équicontinuité des solutions par rapport à la variable d'espace." @default.
- W3100836443 created "2020-11-23" @default.
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- W3100836443 date "2018-02-01" @default.
- W3100836443 modified "2023-10-18" @default.
- W3100836443 title "Homogenization of pathwise Hamilton–Jacobi equations" @default.
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- W3100836443 doi "https://doi.org/10.1016/j.matpur.2017.07.012" @default.
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