具有Dirichlet分数阶拉普拉斯算子的logistic型方程的渐近性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2019-05-05 DOI:10.57262/ade028-0304-169

Tomasz Klimsiak

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引用次数: 2

摘要

我们研究了分数拉普拉斯算子的逻辑型方程的解随着时间到无穷大和非线性部分的指数到无穷大的渐近性。我们证明了能量空间中解的强收敛性和障碍问题解的一致收敛性。作为副产品，我们还证明了爆炸势扰动下Dirichlet分数拉普拉斯算子本征值的截止性质。

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Asymptotics for logistic-type equations with Dirichlet fractional Laplace operator

We study the asymptotics of solutions of logistic type equations with fractional Laplacian as time goes to infinity and as the exponent in nonlinear part goes to infinity. We prove strong convergence of solutions in the energy space and uniform convergence to the solution of an obstacle problem. As a by-product, we also prove the cut-off property for eigenvalues of the Dirichlet fractional Laplace operator perturbed by exploding potentials.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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