Premium
A 2D kernel determination problem in a visco‐elastic porous medium with a weakly horizontally inhomogeneity
Author(s) -
Durdiev Durdimurod Kalandarovich,
Rahmonov Askar Ahmadovich
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6544
Subject(s) - mathematics , mathematical analysis , boundary value problem , viscoelasticity , kernel (algebra) , neumann boundary condition , porous medium , impulse (physics) , work (physics) , boundary (topology) , oscillation (cell signaling) , porosity , physics , classical mechanics , pure mathematics , materials science , thermodynamics , genetics , biology , composite material
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 )= K 0 ( t )+ ϵ x K 1 ( t )+…, where ϵ is a small parameter. In this work, we construct a method for finding K 0 , K 1 up to a correction of the order of O ( ϵ 2 ).