English

The regularity properties of nonlocal abstract wave equations

Analysis of PDEs 2019-08-27 v1

Abstract

In this paper, the regularity properties of Cauchy problem for linear and nonlinear nonlocal wave equations are studied.The equation involves a convolution integral operators with a general kernel operator functions whose Fourier transform are operator functions defined in Hilbert space H together with some growth conditions. We establish local and global existence and uniqueness of solutions assuming enough smoothness on the initial data and the operator functions. By selecting the space H and the operators, the wide class of wave equations in the field of physics are obtained.

Keywords

Cite

@article{arxiv.1908.09759,
  title  = {The regularity properties of nonlocal abstract wave equations},
  author = {Veli Shakhmurov},
  journal= {arXiv preprint arXiv:1908.09759},
  year   = {2019}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1903.01553, arXiv:1706.00813, arXiv:1901.04589, arXiv:1707.04492

R2 v1 2026-06-23T10:57:04.044Z