Behavior of solutions to semilinear evolution inequalities in an annulus: The critical cases

被引：0
|
作者：
Borikhanov, Meiirkhan B. [1 ,2 ]
Torebek, Berikbol T. [2 ,3 ]
机构：
[1] Khoja Akhmet Yassawi Int Kazakh Turkish Univ, Sattarkhanov ave,29, Turkistan 161200, Kazakhstan
[2] Inst Math & Math Modeling, 125 Pushkin Str, Alma Ata 050010, Kazakhstan
[3] Univ Ghent, Dept Math Anal Log & Discrete Math, Ghent, Belgium
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 536卷 / 01期
关键词：
Parabolic equations; Hyperbolic equations; Critical exponent; Global solutions; REACTION-DIFFUSION EQUATIONS; BOUNDARY-VALUE-PROBLEMS; BLOW-UP; GLOBAL-SOLUTIONS; CRITICAL EXPONENT; NONEXISTENCE; EXISTENCE; SYSTEMS; DOMAINS;
D O I：
10.1016/j.jmaa.2024.128172
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper, we consider the parabolic and hyperbolic inequalities with singular potentials and with critical nonlinearities in the annulus domain. The problems are studied with Neumann -type and Dirichlet-type boundary conditions on the boundary. Moreover, we study the systems of problems too. We have proved that the above problems are globally unsolvable in critical cases, thereby filling the gaps the recent results by Jleli and Samet in [J. Math. Anal. Appl. 514: 2 (2022)] and in [Anal. Math. Phys. 12: 90 (2022)]. Proofs are carried out using the method of test functions with logarithmic arguments, which is being developed for the first time in bounded domains. (c) 2024 Elsevier Inc. All rights reserved.
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页数：24
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