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arXiv · 2303.06415

Stochastic homogenization of nonconvex viscous Hamilton-Jacobi equations in one space dimension

Andrea Davini·Elena Kosygina·Atilla Yilmaz
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Abstract

We prove homogenization for viscous Hamilton-Jacobi equations with a Hamiltonian of the form $G(p)+V(x,\omega)$ for a wide class of stationary ergodic random media in one space dimension. The momentum part $G(p)$ of the Hamiltonian is a general (nonconvex) continuous function with superlinear growth at infinity, and the potential $V(x,\omega)$ is bounded and Lipschitz continuous. The class of random media we consider is defined by an explicit hill and valley condition on the diffusivity-potential pair which is fulfilled as long as the environment is not ``rigid''.

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Andrea Davini, Elena Kosygina, Atilla Yilmaz. 2023-03-11. Stochastic homogenization of nonconvex viscous Hamilton-Jacobi equations in one space dimension. https://arxiv.org/abs/2303.06415

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