Nonexistence of solutions to fractional parabolic problem with general nonlinearities

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2023_rcmps2_zhang_nonexistence.pdf (278.92 KB)
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URI: http://hdl.handle.net/10347/31268
ISSN: 0009-725X
E-ISSN: 1973-4409
DOI: 10.1007/s12215-023-00932-1

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2023-07-17

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Springer
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In this content, we investigate a class of fractional parabolic equation with general nonlinearities ∂z(x, t) ∂t − ( + λ) β 2 z(x, t) = a(x1) 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.

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Fractional parabolic equation| General nonlinearity| Tempered fractional Laplacian| Monotonicity

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Rend. Circ. Mat. Palermo, II. Ser (2023)

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The research of Zhang has been partially supported by National Natural Science Foun dation of China(No. 12001344) and the Graduate Education and Teaching Innovation Project of Shanxi, China (No. 2022YJJG124), the research of Nieto has been partially supported by the Agencia Estatal de Investigación (AEI) of Spain under Grant PID2020-113275GB-I00, cofinanced by the European Community fund FEDER, as well as Xunta de Galicia grant ED431C 2019/02 for Competitive Reference Research Groups (2019–22) and the research of Wang has been partially supported by Natural Science Foundation of Shanxi Province, China(No. 20210302123339)

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© The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made
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Estatística, Análise Matemática e Optimización