Blow-up in a p-Laplacian mutualistic model based on graphs

被引：1

作者：

Zhou, Ling ^{[1
]}

Liu, Zuhan ^{[1
]}

机构：

[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 12期

基金：

中国国家自然科学基金;

关键词：

p; -Laplacian; network; blow-up; strong mutualistic systems; comparison principle;

D O I：

10.3934/math.20231444

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a p-Laplacian (p > 2) reaction-diffusion system based on weighted graphs that is used to describe a network mutualistic model of population ecology. After overcoming difficulties caused by the nonlinear p-Laplacian, we develop a new strong mutualistic condition, and the blow-up properties of the solution for any nontrivial initial data are proved under this condition. In this sense, we extend the blow-up results of models with a graph Laplacian (p = 2) to a general graph p-Laplacian.

引用

页码：28210 / 28218

页数：9

共 12 条

[1]

[Anonymous], 2006, Self-Organization in Complex Ecosystems

[2]

Bauer F, 2015, J DIFFER GEOM, V99, P359

[3] The second eigenvalue of the fractional p-Laplacian [J].

Brasco, Lorenzo ;

Parini, Enea .

ADVANCES IN CALCULUS OF VARIATIONS, 2016, 9 (04) :323-355

[4] Yamabe type equations on graphs [J].

Grigor'yan, Alexander ;

Lin, Yong ;

Yang, Yunyan .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (09) :4924-4943

[5] Blowup in a three-species cooperating model [J].

Kim, KK ;

Lin, ZG .

APPLIED MATHEMATICS LETTERS, 2004, 17 (01) :89-94

[6]

Lindqvist P., 2017, Notes on the p-Laplace equation

[7] ON A NETWORK MODEL OF TWO COMPETITORS WITH APPLICATIONS TO THE INVASION AND COMPETITION OF AEDES ALBOPICTUS AND AEDES AEGYPTI MOSQUITOES IN THE UNITED STATES [J].

Liu, Zuhan ;

Tian, Canrong ;

Ruan, Shigui .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2020, 80 (02) :929-950

[8] Blow-up in a network mutualistic model [J].

Liu, Zuhan ;

Chen, Jing ;

Tian, Canrong .

APPLIED MATHEMATICS LETTERS, 2020, 106

[9] Epidemic processes in complex networks [J].

Pastor-Satorras, Romualdo ;

Castellano, Claudio ;

Van Mieghem, Piet ;

Vespignani, Alessandro .

REVIEWS OF MODERN PHYSICS, 2015, 87 (03) :925-979

[10] Global stability of a networked predator-prey model [J].

Tian, Canrong .

APPLIED MATHEMATICS LETTERS, 2023, 143

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