تقرير
Strong well-posedness and separation properties for a bulk-surface convective Cahn--Hilliard system with singular potentials
| العنوان: | Strong well-posedness and separation properties for a bulk-surface convective Cahn--Hilliard system with singular potentials |
|---|---|
| المؤلفون: | Knopf, Patrik, Stange, Jonas |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematical Physics, 35K35, 35D30, 35A01, 35A02, 35Q92, 35B65 |
| الوصف: | This paper addresses the well-posedness of a general class of bulk-surface convective Cahn--Hilliard systems with singular potentials. For this model, we first prove the existence of a global-in-time weak solution by approximating the singular potentials via a Yosida approximation, applying the corresponding results for regular potentials, and eventually passing to the limit in this approximation scheme. Then, we prove the uniqueness of weak solutions and its continuous dependence on the velocity fields and the initial data. Afterwards, assuming additional regularity of the domain as well as the velocity fields, we establish higher regularity properties of weak solutions and eventually the existence of strong solutions. In the end, we discuss strict separation properties for logarithmic type potentials in both two and three dimensions. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.14089 |
| رقم الأكسشن: | edsarx.2407.14089 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |