Behavior of solutions to semilinear evolution inequalities in an annulus: The critical cases
Borikhanov M.B. Torebek B.T.
1 August 2024Academic Press Inc.
Journal of Mathematical Analysis and Applications
2024#536Issue 1
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.
Critical exponent , Global solutions , Hyperbolic equations , Parabolic equations
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Khoja Akhmet Yassawi International Kazakh–Turkish University, Sattarkhanov ave., 29, Turkistan, 161200, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium
Khoja Akhmet Yassawi International Kazakh–Turkish University
Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
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