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Pré-Publication, Document De Travail Année : 2018

Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians

Résumé

We show that the initial value problem for Hamilton-Jacobi equations with multiplicative rough time dependence, typically stochastic, and convex Hamiltonians satisfies finite speed of propagation. We prove that in general the range of dependence is bounded by a multiple of the length of the "skeleton" of the path, that is a piecewise linear path obtained by connecting the successive extrema of the original one. When the driving path is a Brownian motion, we prove that its skeleton has almost surely finite length. We also discuss the optimality of the estimate.
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Dates et versions

hal-01936387 , version 1 (27-11-2018)

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Paul Gassiat, Benjamin Gess, Pierre Louis Lions, Panagiotis E. Souganidis. Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians. 2018. ⟨hal-01936387⟩
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