Geodesic
Inverse problem for a system of integro-differential equations for SH waves in a visco-elastic porous medium: Global solvability
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 491-506 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, hyperbolic equation, global solvability, weight function.
Mots-clés : kernel, Lame coefficient 
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     title = {Inverse problem for a~system of integro-differential equations for {SH} waves in a~visco-elastic porous medium: {Global} solvability},
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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. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 491-506. http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a8/

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