A 2D kernel determination problem in a visco‐elastic porous medium with a weakly horizontally inhomogeneity

We consider a system of hyperbolic integro‐differential equations of SH waves in a visco‐elastic porous medium. In this work, it is assumed that the visco‐elastic porous medium has weakly horizontally inhomogeneity. The direct problem is the initial‐boundary problem: the initial data is equal to zer...

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Published inMathematical methods in the applied sciences Vol. 43; no. 15; pp. 8776 - 8796
Main Authors Durdiev, Durdimurod Kalandarovich, Rahmonov, Askar Ahmadovich
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 01.10.2020
Subjects
Boundary conditions
delta function
Differential equations
hyperbolic equation
Inhomogeneity
inverse problem
kernel
Kernels
Porous media
SH waves
stability
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Summary:We consider a system of hyperbolic integro‐differential equations of SH waves in a visco‐elastic porous medium. In this work, it is assumed that the visco‐elastic porous medium has weakly horizontally inhomogeneity. The direct problem is the initial‐boundary problem: the initial data is equal to zero, and the Neumann‐type boundary condition is specified at the half‐plane boundary and is an impulse function. As additional information, the oscillation mode of the half‐plane line is given. It is assumed that the unknown kernel has the form K(x,t)=K0(t)+ϵxK1(t)+…, where ϵ is a small parameter. In this work, we construct a method for finding K0,K1 up to a correction of the order of O(ϵ2).
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6544