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The Regularity Properties and Blow-up of Solutions for Nonlocal Wave Equations and Applications

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Abstract

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.

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Authors and Affiliations

  1. Department of Industrial Engineering, Antalya Bilim University, 07190, Antalya, Dosemealti, Turkey

    Veli Shakhmurov

  2. Center of Analytical-Information Resource, Azerbaijan State Economic University, 194 M. Mukhtarov, AZ1001, Baku, Azerbaijan

    Veli Shakhmurov

  3. University of Alabama, AL, Tuscaloosa, 35487, USA

    Rishad Shahmurov

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  1. Veli Shakhmurov
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Correspondence to Veli Shakhmurov.

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Shakhmurov, V., Shahmurov, R. The Regularity Properties and Blow-up of Solutions for Nonlocal Wave Equations and Applications. Results Math 77, 229 (2022). https://doi.org/10.1007/s00025-022-01752-y

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