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Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
Open Mathematics, 2017 We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph
Golovaty Yuriy, Flyud Volodymyr
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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 $(0, 1)$ $$ w_{tt} - (x^ w_x)_x = p(t) (x) w, $$ 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.
Piermarco Cannarsa +2 more
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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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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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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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Nonlocal problems for hyperbolic equations with degenerate integral conditions
Electronic Journal of Differential Equations, 2016 In this article, we consider a problem for hyperbolic equation with standard initial data and nonlocal condition. A distinct feature of this problem is that the nonlocal second kind integral condition degenerates and turns into a first kind.
Ludmila S. Pulkina
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Nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing [PDF]
Journal of Functional Analysis, 2021 47 ...
Chen, G-QG, Pang, PHC
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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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