On the well-posedness of the kirchhoff string

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August undefined, 2024

WebWe prove the well-posedness in the Hadamard sense (existence, uniqueness and continuous dependence of the local solution upon the initial ... in engineering, Academic … Web10 de nov. de 2005 · The initial boundary value problem is considered for the dynamic string equation . Its solution is found by means of an algorithm, the constituent parts of …

Global well-posedness of Kirchhoff systems - ScienceDirect

WebWe 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 … 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 … sonam shah treize communications

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

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 … WebThe multiplicity of positive solutions for Kirchhoff type equations depending on a nonnegative parameter Web开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 sonam sheth

Global well-posedness of Kirchhoff systems☆ - Semantic Scholar

On the Gevrey well-posedness of the Kirchhoff equation

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 Web28 de fev. de 1991 · TL;DR: In this article, the authors considered the Cauchy problem for the abstract evolution equation, which describes the Kirchhoff string, and established … sonam srivastava wrightWeb4 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. … small custom signs for home

"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. " - On the well-posedness of the kirchhoff string

On the well-posedness of the kirchhoff string

Asymptotic stability of stationary solutions for the Kirchhoff …

WebEquations proposed in previous work on the non-linear motion of a string show a basic disagreement, which is here traced to an assumption about the longitudinal displacement u. It is shown that it is neither necessary nor justifiable to assume that u is zero; and also that the velocity of propagation of u disturbances in a string is different from that in an infinite … 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 …

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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 … WebAbout Center Leadership Special Committee; People Faculty Postdoc Staff Visitor Graduate; Research Research Areas Seminars Conferences; Programs Undergraduate Graduate

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 ... WebThe aim of this paper is to establish the global well-posedness for Kirchhoff systems. The new approach to the construction of solutions is based on the asymptotic integrations for …

WebThis 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 ... Web20 de nov. de 2024 · The Kirchhoff string and its treatment in scales of Banach spaces 2nd Workshop on Functional-Analytic Methods in Complex Analysis (Trieste) (Singapore: World Scientific) Google Scholar [3] Arosio A and Panizzi S 1996 On the well-posedness of the Kirchhoff string Trans. Am. Math. Soc. 348 305–30. Crossref Google Scholar

Web10 de abr. de 2024 · Abstract. This paper is devoted to proving the almost global solvability of the Cauchy problem for the Kirchhoff equation in the Gevrey space \gamma_ {\eta,L^2}^s. Furthermore, similar results are …

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 … small custom stampWeb1 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 … small custom signsWeb28 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 small custom signs outdoorWeb1 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 asymptotic integrations for strictly hyperbolic systems with time-dependent coefficients. These integrations play an important role to setting the subsequent fixed point argument. sonam phuntsokWeb1 de jan. de 2001 · Global existence and uniform decay rates for the Kirchhoff-Carrier ... Project: Well-Posedness and Asymptotic Behavior of ... which describes small … sonam tashi chodenWeb1 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 = … sonam tashi vs sonam sherpaWebThe above problem without source and dissipative terms is called Kirchhoff-type equation when is not a constant function, which was first introduced by Kirchhoff ; it describes the nonlinear vibrations of an elastic string. up to now, there are numerous results related to global well-posedness, including global existence, decay result, and blow-up properties; … sonam sharma