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Degenerate wave equation

WebThis paper is concerned with the exact boundary controllability for a degenerate and singular wave equation in a bounded interval with a moving endpoint. By the multiplier method and using an adapted Hardy-poincaré inequality, we prove direct and inverse inequalities for the solutions of the associated adjoint equation. As a consequence, by … WebAbstract. We study a wave equation in one space dimension with a general diffusion coefficient which degenerates on part of the boundary. Degeneracy is measured by a real parameter μ a > 0. We establish observability inequalities for weakly (when μ a ∈ [ 0, 1 [) as well as strongly (when μ a ∈ [ 1, 2 [) degenerate equations.

Asymptotic stability and blow-up for the wave equation with …

WebJun 14, 2024 · Use MathJax to format equations. MathJax reference. To learn more, see our tips on writing great answers. Sign up or log in. Sign up using Google Sign up using … Websystem (P) into an augmented system by coupling the degenerate wave equation with a suitable di usion equation and we show the well-posedness of our problem by semigroup theory. In section 3, we prove lack of exponential stability by spectral analysis and by using Bessel functions. In the last section, we prove an optimal decay rate. tri cities washington shooting https://delasnueces.com

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WebKeywords: degenerate wave equation, drift, stabilization, exponential decay MSC: 35L80, 93D23, 93D15 ∗ The author is a member of the Gruppo Nazionale per l’Analisi Matematica, la Proba- This section intends to illustrate the existence of degenerate energy levels in quantum systems studied in different dimensions. The study of one and two-dimensional systems aids the conceptual understanding of more complex systems. In several cases, analytic results can be obtained more easily in the study of one-dimensional systems. For a quantum particle with a wave function moving in a one-dimensional potential , the t… WebOct 10, 2024 · The measurement has determined that we are either in state α 1 or α 2, but not which. Thus there is a partial collapse of the wavefunction onto a linear combination … tri cities washington television providers

Well-posedness for a wave equation with degenerate …

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Degenerate wave equation

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WebIn this paper we establish some regularity results concerning the behavior of weak solutions and very weak solutions of the degenerate wave equation near the boundary. For the nondegenerate case, the correponding results were originally obtained by Fabre and Puel (J. of Diff. Eq. 106, 1993). This kind of results is closely related to the exact ... WebApr 5, 2024 · [17]. We refer to [18, 19, 24] on the decay estimates of degenerate wave equations with localized damping and viscoelastic damping and linear systems with boundary memory dissipation. Most recently, for the research advances on the ground state solutions for quasi-linear equations of Kirchho type and multiple positive solutions to the …

Degenerate wave equation

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WebThis paper studies a fourth-order, nonlinear, doubly-degenerate parabolic equation derived from the thin film equation in spherical geometry. A regularization method is used to study the equation and several useful estimates are obtained. The main http://physics.gmu.edu/~dmaria/590%20Web%20Page/public_html/qm_topics/degenerate/index.html

WebMar 18, 2024 · The ground state has only one wavefunction and no other state has this specific energy; the ground state and the energy level are said to be non-degenerate. However, in the 3-D cubical box potential the energy of a state depends upon the sum of the squares of the quantum numbers (Equation \ref{3D wave}). WebSep 1, 2024 · Boundary controllability for degenerate wave equations. In this section, we prove the exact controllability for the degenerate wave equation (1.1) by the Hilbert …

WebAbstract This work is devoted to studying a wave equation with degenerate nonlo-cal nonlinear damping and source terms. By potential well theory, we show the asymptotic WebSince the equation must hold for all values of x, y and z, and since these coordinates can vary independently of each other, it follows that each term on the left must equal a constant. ... We say that the excited state is "degenerate", i.e., there are three sets of quantum numbers which give the same energy. Degeneracy in energy is generally ...

WebJan 28, 2024 · In this work, we are concerned with the study of stabilization of one-dimensional weakly degenerate wave equation utt − (xγux)x = 0 with x ∈ (0, 1) and γ ∈ [0, 1), controlled by a fractional boundary feedback acting at x = 0. Strong, uniform, and …

http://www.hyperphysics.phy-astr.gsu.edu/hbase/quantum/qnsch.html tri cities wa shootingWebdegenerate wave equation 577 As will be shown in Section 3, it follows that R(s,w(s)) tends to 0 exponentially as s ! 1. Noting this and the fact that krwk2 L2(⌦) w is a monotone operator, we prove that the accumulation points of a solution curve {w(s)} s0 are contained in the set S = {w 2 H1 0 (⌦) krwk2 L2 w + 1 2 w = 0}. terminator pest control wiWebMay 21, 2015 · We study a wave equation in one space dimension with a general diffusion coefficient which degenerates on part of the boundary. Degeneracy is measured by a … terminator picture galleryWebsystem (P) into an augmented system by coupling the degenerate wave equation with a suitable di usion equation and we show the well-posedness of our problem by semigroup theory. In section 3, uniqueness of strong and weak solutions of the system, when we used Hille-Yosida Theorem. In section 4, we prove tri cities washington lodgingWebFeb 1, 2024 · The aim of this paper is to analyze the long-time dynamical behavior of the solution for a degenerate wave equation with time-dependent damping term ∂ t t u + β … tri cities washington homes for saleWebSep 30, 2024 · They also showed the global existence of solutions under critical initial conditions. In , the authors studied the following damped degenerate Kirchhoff equation: where . The global existence, behavior of solutions, and blow-up in time for are obtained, under appropriate assumptions. In , the IBVP of Kirchhoff wave equation is considered. terminator police shootout sceneWebMar 1, 2024 · DOI: 10.1016/j.jmaa.2024.127267 Corpus ID: 257832573; Bistable Traveling Waves in Degenerate Competitive Systems @article{Lin2024BistableTW, title={Bistable Traveling Waves in Degenerate Competitive Systems}, author={Guo Lin and Yanli Huang}, journal={Journal of Mathematical Analysis and Applications}, year={2024} } terminator plasma weapons