基于稳定性结果的线性增长进化Neumann问题的存在性

IF 0.9 4区数学 Q2 Mathematics

Annales Academiae Scientiarum Fennicae-Mathematica Pub Date : 2019-06-01 DOI:10.5186/AASFM.2019.4461

Leah Schätzler

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引用次数: 0

摘要

摘要研究抛物型系统∂tu - div(Dξf(x,Du)) = - Dug(x, u)的Neumann型边值问题，其中u是向量值，f满足线性增长条件，ξ 7→f(x， ξ)是凸的。我们证明了这种系统的变分解可以用∂tu−div(Dξf(x,Du)) =−Dug(x, u)的变分解近似，且p > 1。这可以解释为具有线性增长的一般流的稳定性和存在性结果。

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Existence for evolutionary Neumann problems with linear growth by stability results

Abstract. We are concerned with the Neumann type boundary value problem to parabolic systems ∂tu− div(Dξf(x,Du)) = −Dug(x, u), where u is vector-valued, f satisfies a linear growth condition and ξ 7→ f(x, ξ) is convex. We prove that variational solutions of such systems can be approximated by variational solutions to ∂tu− div(Dξf(x,Du)) = −Dug(x, u) with p > 1. This can be interpreted both as a stability and existence result for general flows with linear growth.

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来源期刊

Annales Academiae Scientiarum Fennicae-Mathematica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annales Academiæ Scientiarum Fennicæ Mathematica is published by Academia Scientiarum Fennica since 1941. It was founded and edited, until 1974, by P.J. Myrberg. Its editor is Olli Martio. AASF publishes refereed papers in all fields of mathematics with emphasis on analysis.