2024 On the well-posedness of the kirchhoff string

On the well-posedness of the kirchhoff string

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August undefined, 2024

WebAbstract. We consider the Kirchhoff equation ∂ t t u − Δ u ( 1 + ∫ T d ∇ u 2) = 0 on the d -dimensional torus T d, and its Cauchy problem with initial data u ( 0, x), ∂ t u ( 0, x) of size ε in the Sobolev class. The effective equation for the dynamics at the quintic order, obtained in previous papers by quasilinear normal form ... WebIn this article we study the existence and uniqueness of local solutions for the initial-boundary value problem for the Kirchhoff equation u′′ −M(t, ‖u(t)‖)∆u+ u = f in Ω× (0, …

Global well-posedness of Kirchhoff systems - ScienceDirect

Web10 de jun. de 2024 · PDF In this paper, we investigate vibration control for an axially moving Kirchhoff string. ... section III, the well posedness and the global stability of the closed-loop system are established. WebAbstract We study the 2D linear wave equation with dynamical control on the boundary. New mathematical difficulties appear due to the boundary conditions. By adding some artificial viscosity term, ... office depot investor relations

On the Gevrey well-posedness of the Kirchhoff equation

WebThis paper considers nonlinear Kirchhoff equation with Kelvin–Voigt damping. This model is used to describe the transversal motion of a stretched string. The existence of smooth stationary solutions of nonlinear Kirchhoff equation has been studied widely. In the present contribution, we prove that a class of stationary solutions is asymptotic stable by … Web16 de jul. de 2024 · We investigate well-posedness, regularity and asymptotic behavior of parabolic Kirchhoff equations on bounded domains of , N ⩾ 2, with non-homogeneous … Web30 de set. de 2024 · This paper is concerned with the well-posedness as well as the asymptotic behavior of solutions for a quasi-linear Kirchhoff wave model with nonlocal … office depot inventory check

On the mildly degenerate Kirchhoff string - Arosio - 1991 ...

Parabolic Kirchhoff equations with non-homogeneous flux …

WebThe Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. WebOn the Well-Posedness of the Kirchhoff String @article{Arosio1996OnTW, title={On the Well-Posedness of the Kirchhoff String}, author={Alberto Daniele Arosio and Stefano … my christmas list 2018Web21 de ago. de 2015 · This paper is devoted to proving the almost global solvability of the Cauchy problem for the Kirchhoff equation in the Gevrey space $γ^s_{η,L^2}$. … office depot in ventura ca

"Web1 de ago. de 2024 · Abstract. In this work, the initial-boundary value problem is considered for the dynamic Kirchhoff string equation u t ⁢ t-(α ⁢ (t) + β ⁢ ∫-1 1 u x 2 ⁢ d x) ⁢ u x ⁢ x = f.Here α ⁢ (t) is a continuously differentiable function, α ⁢ (t) ≥ c 0 > 0 and 𝛽 is a positive constant. For solving this problem approximately, a symmetric three-layer semi-discrete scheme with ... " - On the well-posedness of the kirchhoff string

On the well-posedness of the kirchhoff string

Asymptotic stability of stationary solutions for the Kirchhoff …

Web30 de set. de 2024 · This paper is concerned with the well-posedness as well as the asymptotic behavior of solutions for a quasi-linear Kirchhoff wave model with nonlocal nonlinear damping term $ \sigma\left ... On the well-posedness of the Kirchhoff string, Trans. Amer. Math. Soc., 348 (1996), 305-330. doi: 10.1090/S0002 ... Web16 de jul. de 2024 · We investigate well-posedness, regularity and asymptotic behavior of parabolic Kirchhoff equations on bounded domains of , N ⩾ 2, with non-homogeneous flux boundary conditions of Neumann or Robin type. The data in the problem satisfy (f, g, u(0)) ∈ L 2 (Ω) × L 2 (∂Ω) × H 1 (Ω).Approximated solutions are constructed using time …

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Web16 de abr. de 2014 · In this paper the existence of infinitely many solutions for a class of Kirchhoff-type problems involving the p-Laplacian, with p > 1, is established. By using … WebWe prove the well-posedness in the Hadamard sense (existence, uniqueness and continuous dependence of the local solution upon the initial ... in engineering, Academic …

Web3 Well-posedness 17 1. Introduction The nonlinear vibrations of an elastic string are written in the form of partial integro-diﬀerential equations by ρh ∂2u ∂t2 = p0 + Eh 2L ZL 0 ∂u ∂x 2 dx! ∂2u ∂x2 +f, (1.1) for 0 WebFollowing physical considerations, we allow m(·) to be any non-decreasing, non-negative continuous function (a degenerate Kirchhoff string). We assume that the initial value u 0 satisfies: m (〈 Au 0 , u 0 〉)>0 (a mildly degenerate Kirchhoff string), that m is locally Lipschitz continuous in the open region where it does not vanish, and that m has a finite …

Web12 de jan. de 2016 · We consider Kirchhoff equations with strong damping, namely with a friction term which depends on a power of the “elastic” operator. We address local and … Web1 de ago. de 2013 · The aim of this paper is to establish the H 1 global well-posedness for Kirchhoff systems. The new approach to the construction of solutions is based on the …

Web10 de fev. de 1998 · The Kirchhoff quasilinear hyperbolic equation. Abstract Nonlinear Wave Equations, Lecture Notes in Mathematics, 507, Springer-Verlag, Berlin ( 1976) On local solutions of some quasilinear degenerate hyperbolic equations. Funkcial.

WebAbstract. The initial boundary value problem for a hyperbolic-type quasilinear equation w t t = φ ( ∫ 0 π w x 2 d x) w x x is considered. Its solution is derived by means of a numerical … office depot in vistaWebThis paper is devoted to proving the almost global solvability of the Cauchy problem for the Kirchhoff equation in the Gevrey space γη,L2s\documentclass[12pt]{minimal} \usepackage ... {Matsuyama2024OnTG, title={On the Gevrey well-posedness of the Kirchhoff equation}, author={Tokio Matsuyama and Michael Ruzhansky}, journal={Journal d ... office depot in viera westWeb4 de mar. de 2024 · Existence and asymptotic behavior of normalized solutions for the modified Kirchhoff equations in. R. 3. Zhongxiang Wang , Business School, University of Shanghai for Science and Technology, Shanghai, 200093, China. Received: 01 October 2024 Revised: 27 January 2024 Accepted: 07 February 2024 Published: 04 March 2024. … office depot in victorWeb5 de abr. de 2024 · In this paper, we prove the global well-posedness for the incompressible magnetohydrodynamics (MHD) equations in the three-dimensional unbounded domain Ω:=R+×R2. office depot in tullahomaWeb28 de ago. de 2007 · Arosio A. and Panizzi S. (1996). On the well-posedness of the Kirchhoff string. Trans. Am. Math. Soc. 348: 305–330 Article MATH MathSciNet Google Scholar Bilbao S. and Smith J.O. (2005). Energy conserving finite difference schemes for nonlinear strings. Acustica 91: 299–311 Google Scholar my christmas love movie castWeb20 de nov. de 2024 · Ground State and Multiple Solutions for Kirchhoff Type Equations With Critical Exponent - Volume 61 Issue 2. Skip to main content Accessibility help ... On the well-posedness ofthe Kirchhoff string. Trans. Amer. Math. Soc. 348 (1996), 305 ... my christmas list cross stitch silver creekWebAbout Center Leadership Special Committee; People Faculty Postdoc Staff Visitor Graduate; Research Research Areas Seminars Conferences; Programs Undergraduate Graduate office depot invitation kits