Ergodicity of a nonlinear stochastic reaction–diffusion equation with memory

Nguyen, Hung D.

doi:10.1016/j.spa.2022.10.005

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Moment Bounds Of the Solutions1

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2023

2024

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Cited by 4 publications

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“…where p 1 and ε 1 are as in (2.2) and (2.5), respectively. Following the framework of [4,52], we introduce the memory variable η(t; s) given by…”

Section: Moment Bounds Of the Solutionsmentioning

confidence: 99%

The invariant measure of a walking droplet in hydrodynamic pilot–wave theory

Nguyen,

Oza

2024

Nonlinearity

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We study the long time statistics of a walker in a hydrodynamic pilot-wave system, which is a stochastic Langevin dynamics with an external potential and memory kernel. While prior experiments and numerical simulations have indicated that the system may reach a statistically steady state, its long-time behavior has not been studied rigorously. For a broad class of external potentials and pilot-wave forces, we construct the solutions as a dynamics evolving on suitable path spaces. Then, under the assumption that the pilot-wave force is dominated by the potential, we demonstrate that the walker possesses a unique statistical steady state. We conclude by presenting an example of such an invariant measure, as obtained from a numerical simulation of a walker in a harmonic potential.

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“…where p 1 and ε 1 are as in (2.2) and (2.5), respectively. Following the framework of [4,52], we introduce the memory variable η(t; s) given by…”

Section: Moment Bounds Of the Solutionsmentioning

confidence: 99%