具有Dirichlet分数阶拉普拉斯算子的logistic型方程的渐近性

IF 1.5 3区数学 Q1 MATHEMATICS

Advances in Differential Equations 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

Advances in Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely, and of interest to a substantial number of mathematicians working in this area.