تقرير
Solutions to the stochastic thin-film equation for initial values with non-full support
| العنوان: | Solutions to the stochastic thin-film equation for initial values with non-full support |
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| المؤلفون: | Dareiotis, Konstantinos, Gess, Benjamin, Gnann, Manuel V., Sauerbrey, Max |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematics - Probability, 35R60, 76A20 |
| الوصف: | The stochastic thin-film equation with mobility exponent $n\in [\frac{8}{3},3)$ on the one-dimensional torus with multiplicative Stratonovich noise is considered. We show that martingale solutions exist for non-negative initial values. This advances on existing results in three aspects: (1) Non-quadratic mobility with not necessarily strictly positive initial data, (2) Measure-valued initial data, (3) Less spatial regularity of the noise. This is achieved by carrying out a compactness argument based solely on the control of the $\alpha$-entropy dissipation and the conservation of mass. Comment: 36 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2305.06017 |
| رقم الأكسشن: | edsarx.2305.06017 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |