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Bilinear Control of a Degenerate Hyperbolic Equation
SIAM Journal on Mathematical Analysis, 2023 We consider the linear degenerate wave equation, on the interval $(0, 1)$ $$ w_{tt} - (x^αw_x)_x = p(t) μ(x) w, $$ with bilinear control $p$ and Neumann boundary conditions. We study the controllability of this nonlinear control system, locally around a constant reference trajectory, the ground state. We prove that, generically with respect to $μ$, any
Piermarco Cannarsa, Cristina Urbani
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Об одной смешанной задаче для вырождающегося гиперболического уравнения третьего порядка
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2023 В работе исследуется смешанная краевая задача для гиперболического уравнения третьего порядка с вырождением порядка внутри области. В положительной части области рассматриваемое уравнение совпадает с уравнением Аллера, которое является уравнением ...
Макаова, Р.Х.
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Decay of solutions of a degenerate hyperbolic equation
Electronic Journal of Differential Equations, 1998 This article studies the asymptotic behavior of solutions to the damped, non-linear wave equation $$ ddot u +gamma dot u -m(|abla u|^2)Delta u = f(x,t),, $$ which is known as degenerate if the greatest lower bound for $m$ is zero, and non-degenerate if ...
Julio G. Dix
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Bitsadze-Samarskii Type Problem for the Diffusion Equation and Degenerate Hyperbolic Equation
Vestnik KRAUNC: Fiziko-Matematičeskie NaukiA boundary value problem of the Bitsadze-Samarskii type is studied in the article for a fractionalorder diffusion equation and a degenerate hyperbolic equation with singular coefficients at lower terms in an unbounded domain.
Ruziev, M.Kh. +3 more
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Global attractor for degenerate damped hyperbolic equations
Journal of Mathematical Analysis and Applications, 2017 This paper deals with the asymptotic behavior of the solutins of the following problem: \[ \partial_{tt} u(x,t) +\beta u_t(x,t) =\mathcal{L} u(x,t) + f(u(x,t)) \quad x\in \Omega, \;t>0 \] \[ u(x,t) =0 \quad x\in \partial \Omega, \;t>0 \] and \[ u(x,0)=u_0(x), \;\;u_t(x,0) = u_1(x), \quad x\in \Omega, \] where \(\Omega\) is bounded domain in \(\mathbb{R}
Chunyou Sun
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Inner boundary value problem with displacement for a second order mixed parabolic-hyperbolic equation [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 This paper investigates inner boundary value problems with a shift for a second-order mixed-hyperbolic equation consisting of a wave operator in one part of the domain and a degenerate hyperbolic operator of the first kind in the other part.
Zh.A. Balkizov +2 more
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The problem with shift for a degenerate hyperbolic equation of the first kind [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2021 For a degenerate first-order hyperbolic equation of the second order containing a term with a lower derivative, we study two boundary value problems with an offset that generalize the well-known first and second Darboux problems. Theorems on an existence
Zhiraslan A. Balkizov
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Advances in Nonlinear Analysis, 2022 This article focuses on the singularity formation of smooth solutions for a one-dimensional nonlinear degenerate hyperbolic-parabolic coupled system originating from the Poiseuille flow of nematic liquid crystals.
Hu Yanbo
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On Behavior of Solution of Degenerated Hyperbolic Equation [PDF]
ISRN Applied Mathematics, 2012 The purpose of this paper is to learn some features of hyperbolic type of nonlinear equations. It is shown that the solution of the equation approaches to the endlessness in the inside of some initial conditions and time of the special marks. The local existence of the equation’s solution has been proved and the problem of unlimited increasing on the ...
Gadjiev, Tahir +2 more
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BOUNDARY CONTROL PROBLEM FOR ONE DEGENERATE HIBERBOLIC EQUATION [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2019 The paper studies the boundary control problem for a degenerate second-order hyperbolic equation. Necessary and sufficient conditions are established for minimal time controllability over Cauchy data.
Attaev A. Kh.
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