Nonexistence of solutions to fractional parabolic problem with general nonlinearities

被引：2

作者：

Zhang, Lihong ^{[1
]}

Liu, Yuchuan ^{[1
]}

Nieto, Juan J. ^{[2
]}

Wang, Guotao ^{[1
]}

机构：

[1] Shanxi Normal Univ, Sch Math & Comp Sci, Taiyuan 030031, Shanxi, Peoples R China

[2] Univ Santiago De Compostela, Dept Estat Anal Matemat & Optimizac, CITMAga, Santiago De Compostela 15782, Spain

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2024年 / 73卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Fractional parabolic equation; General nonlinearity; Tempered fractional Laplacian; Monotonicity; RADIAL SYMMETRY; EQUATIONS; THEOREMS;

D O I：

10.1007/s12215-023-00932-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this content, we investigate a class of fractional parabolic equation with general nonlinearities partial derivative z(x,t)/partial derivative t - (Delta + lambda)(beta/2) z (x,t) = a(x(1)) f(z), where a and f are nondecreasing functions. We first prove that the monotone increasing property of the positive solutions in x1 direction. Based on this, nonexistence of the solutions are obtained by using a contradiction argument. We believe these new ideas we introduced will be applied to solve more fractional parabolic problems.

引用

页码：551 / 562

页数：12

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