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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 195, Number 3, Pages 491–506
DOI: https://doi.org/10.4213/tmf9480 (Mi tmf9480) 		 
This article is cited in 45 scientific papers (total in 45 papers)

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
Full-text PDF (442 kB) Citations (45)
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DOI: https://doi.org/10.4213/tmf9480
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.
Received: 06.10.2017
English version:
Theoretical and Mathematical Physics, 2018, Volume 195, Issue 3, Pages 923–937
DOI: https://doi.org/10.1134/S0040577918060090
Bibliographic databases:
Document Type: Article
Language: Russian
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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    • This publication is cited in the following 45 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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