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Blow - up of solutions of wave equation with a nonlinear boundary condition and interior focusing source of variable order of growth
  • Akbar Aliev,
  • Gulshan Shafieva
Akbar Aliev
Azerbaijan National Academy of Sciences Institute of Mathematics and Mechanics

Corresponding Author:aliyevagil@yahoo.com

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Gulshan Shafieva
Baku State University
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In this paper, being investigated an initial - boundary value problem for a one - dimensional wave equation with a nonlinear source of variable order and nonlinear dissipation at the boundary. The existence of a local solution of the problem under consideration is proved. Then the question of the absence of global solutions is investigated. Depending on the relationship between the order of growth of the nonlinear source and the nonlinear boundary dissipation, different results are obtained on the blow - up of weak solutions in a finite time interval.
08 Jun 2022Submitted to Mathematical Methods in the Applied Sciences
09 Jun 2022Assigned to Editor
09 Jun 2022Submission Checks Completed
28 Jun 2022Reviewer(s) Assigned
28 Jun 2022Review(s) Completed, Editorial Evaluation Pending
28 Jun 2022Editorial Decision: Accept
29 Jul 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8572