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.
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