The regularity properties and blow-up of the solutions for nonlocal general wave equations


Shakhmurov V. B., Bayrak V., Shahmurov R.

JOURNAL OF DIFFERENTIAL EQUATIONS, vol.310, pp.138-163, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 310
  • Publication Date: 2022
  • Doi Number: 10.1016/j.jde.2021.12.004
  • Journal Name: JOURNAL OF DIFFERENTIAL EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.138-163
  • Keywords: Wave equations, Hyperbolic equations, Differential operators, Blow-up, Fourier multipliers, GLOBAL EXISTENCE, ELASTICITY
  • Istanbul Technical University Affiliated: Yes

Abstract

In this paper, the Cauchy problem for nonlocal linear and nonlinear wave equations are studied. The equations include the general differential operators. The existence, uniqueness, L-p-regularity properties and blow-up at finite time of solutions of the Cauchy problem is obtained. By choosing differential operators including in equations, the regularity properties of a different type wave equations are studied. (c) 2021 Elsevier Inc. All rights reserved.