在一个单一的Lifshitz-Slyozov-Wagner模型上

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
C. Eichenberg, B. Niethammer, J. Velázquez
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引用次数: 0

摘要

我们研究了具有奇异系数的经典Lifshitz-Slyozov-Wagner平均场模型的适定性,因为它们出现在二维扩散控制生长中。对于Hölder-continuous初始数据,证明了具有有界平均域的全局解的存在唯一性。如果数据只在L L o c q([0,∞))L^q_{地点}[0]\infty 对于某些q >q >q >1,我们建立了一个解的整体存在性,该解具有一般无界的平均域,但在L r(0,T)中,L^r(0,T)对于某些r >r >r取决于模型中的系数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On a singular Lifshitz-Slyozov-Wagner model

We investigate the well-posedness of the classical Lifshitz-Slyozov-Wagner mean-field model for Ostwald ripening with singular coefficients, as they appear, for example in two-dimensional diffusion controlled growth. For Hölder-continuous initial data we prove the existence and uniqueness of a global solution with bounded mean-field. If the data are only in L l o c q ( [ 0 , ) ) L^q_{loc}([0,\infty )) for some q > 1 q>1 we establish global existence of a solution with a mean-field that is in general unbounded but in L r ( 0 , T ) L^r(0,T) for some r > 1 r>1 that depends on the coefficients in the model.

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来源期刊
Quarterly of Applied Mathematics
Quarterly of Applied Mathematics 数学-应用数学
CiteScore
1.90
自引率
12.50%
发文量
31
审稿时长
>12 weeks
期刊介绍: The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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