The Regularity Properties and Blow-up of Solutions for Nonlocal Wave Equations and Applications

Shakhmurov V., Shahmurov R.

RESULTS IN MATHEMATICS, vol.77, no.6, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 77 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.1007/s00025-022-01752-y
  • Journal Name: RESULTS IN MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

In this paper, the Cauchy problem for linear and nonlinear wave equations is studied.The equation involves an abstract operator A in a Hilbert space H and a convolution term. Here, assuming sufficient smoothness on the initial data and on coefficients, the existence, uniqueness, regularity properties, and blow-up of solutions are established in terms of fractional powers of a given sectorial operator A. We obtain the regularity properties of a wide class of wave equations by choosing a space H and an operator A that appear in the field of physics.