Invariance of convex sets for non‐autonomous evolution equations governed by forms
Invariance of convex sets for non‐autonomous evolution equations governed by forms
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由形式控制的非自主演化方程的凸集不变性
DOI：
10.1112/jlms/jdt082
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
El Maati Ouhabaz
中科院分区：
文献类型：
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作者：
Wolfgang Arendt;Dominik Dier;El Maati Ouhabaz
我们考虑一种非自治形式，即稠密且连续地嵌入到另一个Hilbert空间中的Hilbert空间。由与关联的运算符表示。在给定的情况下，人们知道，对于每一种情况，J·L·利昂斯的这一结果都有唯一的解是众所周知的。本文的目的是找出闭凸子集的不变性的一个判据，也就是说，我们给出了一个关于形式的判据，该判据蕴含着任何时候都是恒定的。在的自治情形下，该判据是已知的，甚至等价于不变性，这一结果由Ouhabaz的《闭凸集的不变性和半群的控制判据》，势能分析5(1996)611-625证明。另见欧哈巴兹《论域上热方程的分析》，伦敦数学学会专著。普林斯顿大学出版社，新泽西州普林斯顿，2005。我们给出了非自治Robin边界条件下热方程解的正性和比较的应用。我们还证明了一个拟线性热方程解的正性。
We consider a non-autonomous formwhereis a Hilbert space which is densely and continuously embedded in another Hilbert space. Denote bythe operator associated with. Given, one knows that for eachthere is a unique solutionofThis result by J. L. Lions is well known. The aim of this article is to find a criterion for the invariance of a closed convex subsetof; that is, we give a criterion on the form which implies thatfor allwhenever. In the autonomous case for, the criterion is known and even equivalent to invariance by a result proved by Ouhabaz ‘Invariance of closed convex sets and domination criteria for semigroups’,Potential Anal.5 (1996) 611–625. See also Ouhabaz ‘Analysis of heat equations on domains’, London Mathematical Society Monographs. Princeton University Press, Princeton, NJ, 2005. We give applications to positivity and comparison of solutions to heat equations with non-autonomous Robin boundary conditions. We also prove positivity of the solution to a quasi-linear heat equation.
DOI：
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发表时间：
1996
期刊：
影响因子：
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作者：
E. Ouhabaz
通讯作者：
E. Ouhabaz