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

  • Nəşrin Növü: Article / Article
  • Cild: 77 Say: 6
  • Nəşr tarixi: 2022
  • Doi nömrəsi: 10.1007/s00025-022-01752-y
  • jurnalın adı: RESULTS IN MATHEMATICS
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Adres: Yox

Qısa məlumat

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.