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 … WebWe prove the well-posedness in the Hadamard sense (existence, uniqueness and continuous dependence of the local solution upon the initial ... in engineering, Academic …
On the well-posedness of the kirchhoff string
Did you know?
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 … WebIn 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 …
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 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 asymptotic integrations for strictly hyperbolic systems with time-dependent coefficients. These integrations play an important role to setting the subsequent fixed point argument.
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, … 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.
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 …
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 ... green sage cafe merrimon ashevilleWeb13 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 … green sage cafe downtown ashevilleWebThe 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; … fly worship songWebThe 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. green sage asheville menuWeb20 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 ... green sage cloth napkinsWebAbstract. 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 … flyworship new songsWeb20 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 green sage cafe south asheville nc