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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.16787 |
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| _version_ | 1866910056408154112 |
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| author | Morandotti, Marco Rybka, Piotr Wheeler, Glen |
| author_facet | Morandotti, Marco Rybka, Piotr Wheeler, Glen |
| contents | We show stabilisation of solutions to one-dimensional advective Cahn-Hilliard equation modeling the Langmuir-Blodgett thin films. This problem has the structure of a gradient flow perturbed by a linear term $βu_x$. Through application of an abstract result by Carvalho-Langa-Robinson, we show that for small $β$ the equation has the structure of gradient flow in a weak sense. Combining this with the finite number of steady states implies stabilization of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16787 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stabilization of solutions to a model of Langmuir-Blodgett films Morandotti, Marco Rybka, Piotr Wheeler, Glen Analysis of PDEs 35B40, 35K35, 37L30, 74K35 We show stabilisation of solutions to one-dimensional advective Cahn-Hilliard equation modeling the Langmuir-Blodgett thin films. This problem has the structure of a gradient flow perturbed by a linear term $βu_x$. Through application of an abstract result by Carvalho-Langa-Robinson, we show that for small $β$ the equation has the structure of gradient flow in a weak sense. Combining this with the finite number of steady states implies stabilization of solutions. |
| title | Stabilization of solutions to a model of Langmuir-Blodgett films |
| topic | Analysis of PDEs 35B40, 35K35, 37L30, 74K35 |
| url | https://arxiv.org/abs/2603.16787 |