An inverse problem for generalized Kelvin-Voigt equation with p-Laplacian and damping term

Antontsev S.N. Khompysh K.
August 2021 IOP Publishing Ltd

Inverse Problems
2021 #37 Issue 8

In this paper, we consider the nonlinear inverse problem for generalized Kelvin-Voigt equations with the p-Laplace diffusion and damping term, describing the motion of incompressible viscous fluids. We assume that the damping term in the momentum equation depends on whether its signal is positive or negative, which may realizes the presence of a source or a sink within the system. The investigated inverse problem consists of finding a coefficient f(t) of the right-hand side of the momentum equation, a vector of velocity field v, and a pressure π. An additional information on a solution of the inverse problem is given as integral overdetermination condition. Under several assumptions on the exponents p, m, the coefficients μ, κ, γ, the dimension of the space d, and specified initial data, we prove the existence and uniqueness of the weak solution of the problem.

Damping term , Existence , Inverse problem , Kelvin–Voigt equations , p-Laplacian , Uniqeness

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Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, Russian Federation
CMAFcIO, University of Lisbon, Portugal
Al-Farabi Kazakh National University, Almaty, Kazakhstan

Lavrentyev Institute of Hydrodynamics SB RAS
CMAFcIO
Al-Farabi Kazakh National University

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