JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 卷:325 |
Nonuniqueness of solutions for a singular diffusion problem | |
Article | |
Yao, Zheng'an ; Zhou, Wenshu | |
关键词: singular parabolic equation; weak solution; existence; nonuniqueness; | |
DOI : 10.1016/j.jmaa.2006.01.071 | |
来源: Elsevier | |
【 摘 要 】
In this paper, we consider a singular diffusion problem and show, by constructing a counterexample, that the weak solution to the problem is not unique. The proof consists of several steps. First, we prove that there exists a maximal weak solution to the problem. We show that the support of the continuous maximal weak solution cannot decrease in time. Then we cite an example of a nonnegative continuous function with shrinking support that also solves the problem, and therefore the problem possesses at least two weak solutions for some continuous nonnegative initial data. (c) 2006 Elsevier Inc. All rights reserved.
【 授权许可】
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