تقرير
Convergence Analysis of the Geometric Thin-Film Equation
| العنوان: | Convergence Analysis of the Geometric Thin-Film Equation |
|---|---|
| المؤلفون: | Náraigh, Lennon Ó, Pang, Khang Ee, Smith, Richard J. |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 76A20, 35D30, 46N20 |
| الوصف: | The Geometric Thin-Film equation is a mathematical model of droplet spreading in the long-wave limit, which includes a regularization of the contact-line singularity. We show that the weak formulation of the problem, given initial Radon data, admits solutions that are globally defined for all time and are expressible as push-forwards of Borel measurable functions whose behaviour is governed by a set of ordinary differential equations (ODEs). The existence is first demonstrated in the special case of a finite weighted sum of delta functions whose centres evolve over time -- these are known as `particle solutions'. In the general case, we construct a convergent sequence of particle solutions whose limit yields a solution of the above form. Moreover, we demonstrate that all weak solutions constructed in this way are $1/2$-H\"older continuous in time and are uniquely determined by the initial conditions. Comment: 24 pages, 0 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2207.14175 |
| رقم الأكسشن: | edsarx.2207.14175 |
| قاعدة البيانات: | arXiv |
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