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The Improved Abstract Boussinesq Equations and Application

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Abstract

In this paper, the existence, uniqueness and \(L^{p}\)-regularity properties of solutions of initial value problem for improved abstract Boussinesq equation is obtained. The equation includes a linear operator A in a Banach space E. We can obtain the existence, uniqueness and qualitative properties a different classes improved Boussinesq equations by choosing the space E and linear operator A, which occur in a wide variety of physical systems. By applying this result, initial value problem for nonlocal Boussinesq equations and mixed problem for degenerate Boussinesq equations are studied.

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Authors and Affiliations

  1. Antalya Bilim University, 07190, Antalya, Turkey

    Veli B. Shakhmurov

  2. Azerbaijan State Economic University, Research Center, 1001, Baku, Azerbaijan

    Veli B. Shakhmurov

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

    Rishad Shahmurov

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  1. Veli B. Shakhmurov
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  2. Rishad Shahmurov
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Correspondence to Veli B. Shakhmurov.

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Shakhmurov, V.B., Shahmurov, R. The Improved Abstract Boussinesq Equations and Application. Mediterr. J. Math. 18, 233 (2021). https://doi.org/10.1007/s00009-021-01874-7

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  • DOI: https://doi.org/10.1007/s00009-021-01874-7

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