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A problem of determining a special spatial part of 3D memory kernel in an integro‐differential hyperbolic equation
Author(s) -
Durdiev Umidjon,
Totieva Zhanna
Publication year - 2019
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.5863
Subject(s) - mathematics , mathematical analysis , boundary value problem , kernel (algebra) , initial value problem , hyperbolic partial differential equation , inverse problem , cauchy problem , polynomial , uniqueness , domain (mathematical analysis) , variable (mathematics) , dirac delta function , cauchy distribution , partial differential equation , pure mathematics
The inverse problem of determining 2D spatial part of integral member kernel in integro‐differential wave equation is considered. It is supposed that the unknown function is a trigonometric polynomial with respect to the spatial variable y with coefficients continuous with respect to the variable x . Herein, the direct problem is represented by the initial‐boundary value problem for the half‐space x >0 with the zero initial Cauchy data and Neumann boundary condition as Dirac delta function concentrated on the boundary of the domain ( y , t ) ∈ R 2 , x > 0 . Local existence and uniqueness theorem for the solution to the inverse problem is obtained.