Long Time Behavior of Stochastic Thin Film Equation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910121145139200 |
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| author | Kapustyan, Oleksiy Martynyuk, Olha Misiats, Oleksandr Stanzhytskyi, Oleksandr |
| author_facet | Kapustyan, Oleksiy Martynyuk, Olha Misiats, Oleksandr Stanzhytskyi, Oleksandr |
| contents | We consider the stochastic thin-film equation with linear deterministic and stochastic Itô 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10010 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long Time Behavior of Stochastic Thin Film Equation Kapustyan, Oleksiy Martynyuk, Olha Misiats, Oleksandr Stanzhytskyi, Oleksandr Analysis of PDEs Probability We consider the stochastic thin-film equation with linear deterministic and stochastic Itô 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. |
| title | Long Time Behavior of Stochastic Thin Film Equation |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2604.10010 |