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arXiv · 2604.10010

Long Time Behavior of Stochastic Thin Film Equation

Oleksiy Kapustyan·Olha Martynyuk·Oleksandr Misiats·Oleksandr Stanzhytskyi
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Abstract

We consider the stochastic thin-film equation with linear deterministic and stochastic It\^o perturbations. The existence of nonnegative weak martingale solutions on the semi-axis is established, and their asymptotic behavior as $t \to \infty$ is investigated. It is shown that in square mean the $L^\infty$ norm of the solution converges to the spatial mean value of the initial condition, multiplied by a random factor similar to a geometric Wiener process.

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Oleksiy Kapustyan, Olha Martynyuk, Oleksandr Misiats, Oleksandr Stanzhytskyi. 2026-04-11. Long Time Behavior of Stochastic Thin Film Equation. https://arxiv.org/abs/2604.10010

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