On the well-posedness of the kirchhoff string
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 … 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 …
On the well-posedness of the kirchhoff string
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WebWe prove the well posedness of mixed problems consisting of a system of ordinary differential equations coupled with systems of balance laws in domains with moving … Web13 de fev. de 2024 · Arosio, A. and Panizzi, S. (1996) On the Well-Posedness of the Kirchhoff String. Transactions of the American Mathematical Society, 348, 305-330. …
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 …
Web21 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 $γ^s_{η,L^2}$. … 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 …
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 …
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 … shop small business saturday quotesWebAbstract In this paper, we investigate vibration control for an axially moving Kirchhoff string. ... (PDE-ODE) and a novel energy like function, the well-posedness and exponential stability of the closed-loop system are established by means of the Faedo-Galerkin method and the Lyapunov method. shopsmall comWebWe prove the well-posedness in the Hadamard sense (existence, uniqueness and continuous dependence of the local solution upon the initial ... in engineering, Academic … shop small campaignWeb20 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 ... shop small.comWeb3 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 shop small business saturday 2021Web1 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. shop small business txWeb20 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 shopsmall.com