Asymptotic Radial Solution of Parabolic Tempered Fractional Laplacian Problem

We study parabolic equation with the tempered fractional Laplacian and logarithmic nonlinearity by the direct method of moving planes. We first prove several important theorems, such as asymptotic maximum principle, asymptotic narrow region principle and asymptotic strong maximum principle for antis...

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Bibliographic Details
Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 46; no. 1
Main Authors Wang, Guotao, Liu, Yuchuan, Nieto, Juan J., Zhang, Lihong
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 2023
Springer Nature B.V
Subjects
Applications of Mathematics
Asymptotic properties
Logarithms
Mathematics
Mathematics and Statistics
Maximum principle
Nonlinearity
Logarithmic nonlinearity
35R11
Tempered fractional Laplacian
Fractional parabolic equation
Asymptotic maximum principle
Asymptotic symmetry and monotonicity
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Summary:We study parabolic equation with the tempered fractional Laplacian and logarithmic nonlinearity by the direct method of moving planes. We first prove several important theorems, such as asymptotic maximum principle, asymptotic narrow region principle and asymptotic strong maximum principle for antisymmetric functions, which are critical factors in the process of moving planes. Then, we further derive some properties of asymptotic radial solution to parabolic equation with the tempered fractional Laplacian and logarithmic nonlinearity in a unit ball. These consequences can be applied to investigate more nonlinear nonlocal parabolic equations.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-022-01394-x