Parabolic Obstacle-Type Problems: Regularity, Existence, and Deviation
抛物线障碍类型问题:规律性、存在性和偏差
基本信息
- 批准号:407265145
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:德国
- 项目类别:Research Grants
- 财政年份:2018
- 资助国家:德国
- 起止时间:2017-12-31 至 2021-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The proposed project is aimed at studying several parabolic free boundary problems of obstacle-type. The research program includes issues concerning well-posedness of parabolic problems involving equations with a hysteretic discontinuity in the source term, the study of regularity properties of the free boundary and the qualitative behavior of solutions for the above-mentioned problems, and the derivation of functionals that give realistic fully computable upper bounds of the difference between the exact solutions of the parabolic Signorini problems and any approximative solution regardless of the approximation method.In recent years the proposed research directions become very popular in the world. The regularity topics belong to the mainstream of investigations. Existence and nonexistence results are also not evident, especially for problems with non-variational nature. The estimates of deviation from the exact solution (upper bounds) lie on the crossroad of analytical and numerical studies of free boundary problems.All the suggested problems are new and original. Notice also that for obstacle-type problems the most part of the classical parabolic techniques is not applicable. The reason for this is an absence of any a priori information about the regularity of the free boundary. So, we have to combine ideas from the calculus of variations, some geometrical observations, rescaling and blow-up techniques, analysis of caloric functions and various monotonicity formulas.
该项目旨在研究几个障碍物型抛物自由边界问题。该研究计划包括关于抛物问题的适定性问题,包括在源项中具有滞后间断的方程,自由边界的正则性研究以及上述问题解的定性行为,和推导的泛函,给出现实的完全可计算的上限之间的差异的精确解的抛物Signorini问题和任何近年来,提出的研究方向在国际上非常流行。规律性问题是研究的主流。存在和不存在的结果也不明显,特别是对于非变分性质的问题。对精确解(上界)的偏差估计处于自由边界问题的解析研究和数值研究的交叉点上,所提出的问题都是新的、原创的。还要注意的是,对于障碍型问题,大多数经典的抛物线技术是不适用的。其原因是没有任何先验信息的规则性的自由边界。因此,我们必须将变分法、一些几何观察、重新标度和爆破技术、热函数分析和各种单调性公式的思想联合收割机结合起来。
项目成果
期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Biharmonic Obstacle Problem: Guaranteed and Computable Error Bounds for Approximate Solutions
- DOI:10.1134/s0965542520110032
- 发表时间:2020-11-01
- 期刊:
- 影响因子:0.7
- 作者:Apushkinskaya, D. E.;Repin, S., I
- 通讯作者:Repin, S., I
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Privatdozentin Dr. Darya Apushkinskaya其他文献
Privatdozentin Dr. Darya Apushkinskaya的其他文献
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