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Inverse Problem for A System of Integro-Differential Equations for SH Waves in A Visco-Elastic Porous Medium: Global Solvability

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Abstract

We consider a system of hyperbolic integro-differential equations for SH waves in a visco-elastic porous medium. The inverse problem is to recover a kernel (memory) in the integral term of this system. We reduce this problem to solving a system of integral equations for the unknown functions. We apply the principle of contraction mappings to this system in the space of continuous functions with a weight norm. We prove the global unique solvability of the inverse problem and obtain a stability estimate of a solution of the inverse problem.

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Authors and Affiliations

  1. Bukhara State University, Bukhara, Uzbekistan

    D. K. Durdiev & A. A. Rahmonov

Authors
  1. D. K. Durdiev
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  2. A. A. Rahmonov
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Correspondence to D. K. Durdiev.

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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 195, No. 3, pp. 491–506, June, 2018.

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Durdiev, D.K., Rahmonov, A.A. Inverse Problem for A System of Integro-Differential Equations for SH Waves in A Visco-Elastic Porous Medium: Global Solvability. Theor Math Phys 195, 923–937 (2018). https://doi.org/10.1134/S0040577918060090

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  • DOI: https://doi.org/10.1134/S0040577918060090

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