An inverse problem for Kelvin–Voigt equations perturbed by isotropic diffusion and damping

Kh. Khompysh, Khanat Kenzhebai

2021

Data confidence 70 medium

How this score is calculated

It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.

Abstract

In this paper, we consider an inverse problem of finding a coefficient of right hand side of the following system of Kelvin–Voigt equations perturbed by an isotropic diffusion and damping terms The damping term γ|v|m − 2v in the momentum equation realizes an absorbtion (sink) if γ ≤ 0, and a source if γ > 0. We show how the exponents p, m, the coefficients ν, ϰ, γ, the dimension of the space d, and data of the problem should interact each other for the existence of weak solutions to the problem. We also establish the conditions for uniqueness of the solutions to this problem.