On Local Solutions of a Mildly Degenerate Hyperbolic Equation
Journal of Mathematical Analysis and Applications, 1999 In this paper existence and uniqueness of local solutions for the initial boundary problem associated to a second order hyperbolic equation are established. More precisely, the following problem is considered: \[ \begin{gathered} u_{tt}-M\left(\int_\Omega|Du|^2dx\right)a(x)\Delta u=0\qquad \text{in }\Omega\times\mathbb R_+,\\ u(x,t)\bigl|_{\partial ...
Aassila, Mohammed, Kaya, Dogan
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INITIAL-BOUNDARY VALUE PROBLEM FOR THE DEGENERATE HYPERBOLIC EQUATION OF A HANGING STRING [PDF]
We consider an initial-boundary value problem for the degenerate linear hyperbolic equation as a model of the motion of an inextensible string fixed at one end in the gravity field. We shall show the existence and the uniqueness of the solution and study
Takayama, Masahiro
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Global Weak Solution, Uniqueness and Exponential Decay for a Class of Degenerate Hyperbolic Equation
Communications in Advanced Mathematical Sciences, 2022 This paper deals with existence, uniqueness and energy decay of solutions to a degenerate hyperbolic equations given by \begin{align*} K(x,t)u'' - M\left(\int_\Omega |\nabla u|^2\,dx \right) \Delta u - \Delta u' = 0, \end{align*} with operator ...
Carlos Raposo, Ducival Pereira
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Solvability of a nonlocal problem for a hyperbolic equation with degenerate integral conditions
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2019 In this paper, we consider a nonlocal problem with integral conditions for hyperbolic equation. Close attention focuses on degenerate integral conditions, namely, on the second kind integral conditions which degenerate into the first kind conditions at ...
Ludmila Stepanovna Pulkina +1 more
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Holographic thermal correlators for hyperbolic CFTs
Journal of High Energy Physics, 2023 We use holography to compute the exact form of retarded Green’s functions for a scalar operator with conformal dimension ∆ in a thermal CFT and in its related counterpart with chemical potential in R 1 × H 3.
Atanu Bhatta +3 more
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A class of abstract quasi-linear evolution equations of second order
, 1999 In this paper we study the abstract quasi-linear evolution equation of second order formula here in a general banach space z. it is well-known that the abstract quasi-linear theory due to kato [10, 11] is widely applicable to quasi-linear partial ...
NAOKI TANAKA, Tanaka, Naoki
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Optimal decay-error estimates for the hyperbolic-parabolic singular perturbation of a degenerate nonlinear equation [PDF]
, 2013 We consider a degenerate hyperbolic equation of Kirchhoff type with a small parameter epsilon in front of the second-order time-derivative. In a recent paper, under a suitable assumption on initial data, we proved decay-error estimates for the difference
GHISI, MARINA, GOBBINO, MASSIMO
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A boundary-value problem with shift for a hyperbolic equation degenerate in the interior of a region
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2014 For a degenerate hyperbolic equation in characteristic region (lune) a boundary-value problem with operators of fractional integro-differentiation is studied.
Oleg A Repin, Svetlana K Kumykova
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Degenerate hyperbolic equations with lower degree degeneracy [PDF]
Proceedings of the American Mathematical Society, 2014 Summary: We prove that the Cauchy problem of degenerate hyperbolic equations is well-posed if leading coefficients are degenerate at a low degree.
Han, Qing, Liu, Yannan
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Low Mach Asymptotic Preserving Scheme for the Euler-Korteweg Model [PDF]
, 2013 We present an all speed scheme for the Euler-Korteweg model. We study a semi-implicit time-discretisation which treats the terms, which are stiff for low Mach numbers, implicitly and thereby avoids a dependence of the timestep restriction on the Mach ...
Giesselmann, Jan
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