Generalized Kelvin-Voigt equations for nonhomogeneous and incompressible fluids

Antont︠s︡ev, S. N.; Oliveira, H. B. de; Khompysh, Kh.

doi:10.4310/cms.2019.v17.n7.a7

Cited by 22 publications

(16 citation statements)

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“…Then the function v(t) is a solution of the Cauchy problem: v (t) = 0, v(0) = 0, (v(0) = 0 follows from the condition (7)). This problem has only trivial solution v(t) ≡ 0.…”

Section: Equivalent Problemmentioning

confidence: 99%

An inverse problem for the pseudo-parabolic equation with p-Laplacian

Antont︠s︡ev¹,

Aitzhanov²,

Ashurova³

2022

EECT

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In this article, we study the inverse problem of determining the right side of the pseudo-parabolic equation with a p-Laplacian and nonlocal integral overdetermination condition. The existence of solutions in a local and global time to the inverse problem is proved by using the Galerkin method. Sufficient conditions for blow-up (explosion) of the local solutions in a finite time are derived. The asymptotic behavior of solutions to the inverse problem is studied for large values of time. Sufficient conditions are obtained for the solution to disappear (vanish to identical zero) in a finite time. The limits conditions that which ensure the appropriate behavior of solutions are considered.

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“…Then the function v(t) is a solution of the Cauchy problem: v (t) = 0, v(0) = 0, (v(0) = 0 follows from the condition (7)). This problem has only trivial solution v(t) ≡ 0.…”

Section: Equivalent Problemmentioning

confidence: 99%

An inverse problem for the pseudo-parabolic equation with p-Laplacian

Antont︠s︡ev¹,

Aitzhanov²,

Ashurova³

2022

EECT

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“…The various initial-boundary value problems for the classical linear and nonlinear Kelvin-Voigt equations have been studied by several authors, for instance, in [2], [4][5][6][7][8][9][10][11] for homogenous fluids, i.e. when the density is a known constant, and in [12], for nonhomogeneous fluids, i.e. when the density is unknown function.…”

Section: Int J Math Phys (Online)mentioning

confidence: 99%

AN INITIAL-BOUNDARY VALUE PROBLEM FOR KELVIN-VOIGT EQUATIONS WITH (p(x), q(x),m(x))- STRUCTURE

Khompysh

Kabidoldanova

2022

ijmph

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“…Investigations of the mathematical correctness of such equations are devoted to the works. [14][15][16][32][33][34][35][36][37] In the work of M. O. Korpusov, A. G. Sveshnikov, 21 a model equation is considered that describes the relaxation of an initial perturbation in a crystalline semiconductor in the case when its electrical conductivity depends nonlocally on the field.…”

Section: Introductionmentioning

confidence: 99%

An initial boundary value problem for a pseudoparabolic equation with a nonlinear boundary condition

Antont︠s︡ev

Aitzhanov

Zhanuzakova

2022

Math Methods in App Sciences

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An initial boundary value problem for a quasilinear equation of pseudoparabolic type with a nonlinear boundary condition of the Neumann-Dirichlet type is investigated in this work. From a physical point of view, the initial boundary value problem considered here is a mathematical model of quasistationary processes in semiconductors and magnets, which takes into account a wide variety of physical factors. Many approximate methods are suitable for finding eigenvalues and eigenfunctions in problems where the boundary conditions are linear with respect to the desired function and its derivatives. Among these methods, the Galerkin method leads to the simplest calculations. On the basis of a priori estimates, we prove a local existence theorem and uniqueness for a weak generalized solution of the initial boundary value problem for the quasilinear pseudoparabolic equation. A special place in the theory of nonlinear equations is occupied by the study of unbounded solutions, or, as they are called in another way, blow-up regimes. Nonlinear evolutionary problems admitting unbounded solutions are globally unsolvable. In the article, sufficient conditions for the blow-up of a solution in a finite time in a limited area with a nonlinear Neumann-Dirichlet boundary condition are obtained. KEYWORDS asymptotic behavior of the solution, blow-up of the solution, Galerkin method, nonlinear boundary conditions, pseudoparabolic equations, the existence of a solution, uniqueness of the solution MSC CLASSIFICATION

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Generalized Kelvin-Voigt equations for nonhomogeneous and incompressible fluids

Cited by 22 publications

References 0 publications

An inverse problem for the pseudo-parabolic equation with p-Laplacian

An inverse problem for the pseudo-parabolic equation with p-Laplacian

AN INITIAL-BOUNDARY VALUE PROBLEM FOR KELVIN-VOIGT EQUATIONS WITH (p(x), q(x),m(x))- STRUCTURE

An initial boundary value problem for a pseudoparabolic equation with a nonlinear boundary condition

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