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The Cauchy problem for Boussinesq equations with general elliptic part

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Abstract

In this paper, the existence and uniqueness of solution of the Cauchy problem for abstract Boussinesq equation is obtained. The leading part of the equation include general elliptic operator and abstract positive operator in a Banach space E. Since the Banach space E and linear operators are sufficiently large classes, by choosing their we obtain the existence and uniqueness of solution of numerous classes of generalized Boussinesq type equations which occur in a wide variety of physical systems. By applying this result, the Wentzell–Robin type mixed problem for Boussinesq equations and the Cauchy problem for finite or infinite systems of Boussinesq equations are studied.

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Acknowledgements

The author would like to express a gratitude to Bulent Eryigit for his useful advices in English in preparing of this paper.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Okan University, Akfirat, Tuzla, 34959, Istanbul, Turkey

    Veli B. Shakhmurov

  2. Department of Mathematics, University of Alabama, Tuscaloosa, USA

    Rishad Shahmurov

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  1. Veli B. Shakhmurov
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Correspondence to Veli B. Shakhmurov.

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Shakhmurov, V.B., Shahmurov, R. The Cauchy problem for Boussinesq equations with general elliptic part. Anal.Math.Phys. 9, 1689–1709 (2019). https://doi.org/10.1007/s13324-018-0265-1

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