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arXiv · 1908.09759

The regularity properties of nonlocal abstract wave equations

Veli Shakhmurov
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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.

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Veli Shakhmurov. 2019-08-20. The regularity properties of nonlocal abstract wave equations. https://arxiv.org/abs/1908.09759

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