Integral type Cauchy problem for abstract wave equations and applications

Agarwal R. P., Shakhmurov V. B.

APPLICABLE ANALYSIS, vol.102, no.7, pp.2097-2122, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 102 Issue: 7
  • Publication Date: 2023
  • Doi Number: 10.1080/00036811.2021.2021184
  • Journal Name: APPLICABLE ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.2097-2122
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

We consider the integral type problem for linear and nonlinear abstract wave equations with operator coefficient in E-valued L-p, 1 <= p <= infinity spaces. The equation includes an abstract linear operator A that defined in a Banach space E. Here, the existence, uniqueness, uniform estimates of solution and quality properties of integral wave problem are derived. We also obtain the same properties for solutions of mixed integral problem for nonlocal and anisotropic classes, by choosing the space E and operator A.