On the well-posedness of the kirchhoff string
Web13 de nov. de 2012 · Global Well-Posedness of the Kirchhoff Equation and Kirchhoff Systems. T. Matsuyama, Michael Ruzhansky. Mathematics. 2014. This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be … WebThe 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; …
On the well-posedness of the kirchhoff string
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WebAbstract 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. 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 …
Web5 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. 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 …
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 … 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 ...
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, …
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 chinese id generator redditWebON THE WELL-POSEDNESS OF THE KIRCHHOFF STRING ALBERTO AROSIO AND STEFANO PANIZZI Abstract. Let us consider the Cauchy problem for the quasilinear … chinese imari wareWebIn this paper, we study a highly nonlocal parametric problem involving a fractional-type operator combined with a Kirchhoff-type coefficient. ... Arosio and S. Panizzi, On the … chinese image translationWebAbstract. 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 ... chinese image captionWebFollowing 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 … grand oaks dressage showWebWe 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 … chinese ime microsoftWeb3 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 grand oaks drive crestwood ky