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TMF, 2018, Volume 195, Number 3, Pages 491–506 (Mi tmf9480)  

Inverse problem for a system of integro-differential equations for SH waves in a visco-elastic porous medium: Global solvability

D. K. Durdiev, A. A. Rakhmonov

Bukhara State University, Bukhara, Uzbekistan

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.

Keywords: integro-differential equation, inverse problem, Dirac delta function, kernel, hyperbolic equation, Lame coefficient, global solvability, weight function.

DOI: https://doi.org/10.4213/tmf9480

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English version:
Theoretical and Mathematical Physics, 2018, 195:3, 923–937

Bibliographic databases:

Document Type: Article
Received: 06.10.2017

Citation: D. K. Durdiev, A. A. Rakhmonov, “Inverse problem for a system of integro-differential equations for SH waves in a visco-elastic porous medium: Global solvability”, TMF, 195:3 (2018), 491–506; Theoret. and Math. Phys., 195:3 (2018), 923–937

Citation in format AMSBIB
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