Asymptotic behavior for semi-linear wave equation with weak damping

2013 ◽  
Vol 7 ◽  
pp. 713-718
Author(s):  
D. C. Pereira ◽  
C. A. Raposo
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Weak Damping

scholarly journals Global existence and asymptotic behavior of solutions for a semi-linear wave equation

2012 ◽  
Vol 385 (2) ◽  
pp. 836-853 ◽  
Author(s):  
Yu-Zhu Wang ◽  
Fagui Liu ◽  
Yuanzhang Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Global Existence ◽  
Asymptotic Behavior Of Solutions ◽  
Linear Wave ◽  
Linear Wave Equation

Spatial variation for the solution to the stochastic linear wave equation driven by additive space-time white noise

2018 ◽  
Vol 18 (05) ◽  
pp. 1850036 ◽  
Author(s):  
M. Khalil ◽  
C. A. Tudor ◽  
M. Zili
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
White Noise ◽  
Space Time ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Stochastic Wave Equation ◽  
Quadratic Variations

We study the asymptotic behavior of the spatial quadratic variation for the solution to the stochastic wave equation driven by additive space-time white noise. We prove that the sequence of its renormalized quadratic variations satisfies a central limit theorem (CLT for short). We obtain the rate of convergence for this CLT via the Stein–Malliavin calculus and we also discuss some consequences.

scholarly journals Energy decay rate for a quasi-linear wave equation with localized strong dissipation

2011 ◽  
Vol 62 (1) ◽  
pp. 164-172 ◽  
Author(s):  
Daewook Kim ◽  
Yong Han Kang ◽  
Mi Jin Lee ◽  
Il Hyo Jung
Keyword(s):  
Wave Equation ◽  
Decay Rate ◽  
Energy Decay ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Energy Decay Rate

scholarly journals Parameter identification for the linear wave equation with Robin boundary condition

2019 ◽  
Vol 27 (1) ◽  
pp. 25-41
Author(s):  
Valeria Bacchelli ◽  
Dario Pierotti ◽  
Stefano Micheletti ◽  
Simona Perotto
Keyword(s):  
Wave Equation ◽  
Mixed Boundary ◽  
Stability Result ◽  
Interval Length ◽  
Left Endpoint ◽  
Linear Wave ◽  
Reconstruction Procedure ◽  
Element Discretization ◽  
Linear Wave Equation ◽  
Bounded Interval

Abstract We consider an initial-boundary value problem for the classical linear wave equation, where mixed boundary conditions of Dirichlet and Neumann/Robin type are enforced at the endpoints of a bounded interval. First, by a careful application of the method of characteristics, we derive a closed-form representation of the solution for an impulsive Dirichlet data at the left endpoint, and valid for either a Neumann or a Robin data at the right endpoint. Then we devise a reconstruction procedure for identifying both the interval length and the Robin parameter. We provide a corresponding stability result and verify numerically its performance moving from a finite element discretization.

scholarly journals Analysis of modified Godunov type schemes for the two-dimensional linear wave equation with Coriolis source term on cartesian meshes

2018 ◽  
Vol 373 ◽  
pp. 91-129 ◽  
Author(s):  
Emmanuel Audusse ◽  
Minh Hieu Do ◽  
Pascal Omnes ◽  
Yohan Penel
Keyword(s):  
Wave Equation ◽  
Source Term ◽  
Linear Wave ◽  
Two Dimensional ◽  
Linear Wave Equation ◽  
Cartesian Meshes

Variational Iteration Method and Homotopy-Perturbation Method for Solving Second-Order Non-Linear Wave Equation

2007 ◽  
Author(s):  
A. Barari ◽  
M. Omidvar ◽  
S. Gholitabar ◽  
D. D. Ganji ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Wave Equation ◽  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Second Order ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Variational Iteration ◽  
Homotopy Perturbation

scholarly journals Godunov type scheme for the linear wave equation with Coriolis source term

2017 ◽  
Vol 58 ◽  
pp. 1-26 ◽  
Author(s):  
Emmanuel Audusse ◽  
Stéphane Dellacherie ◽  
Minh Hieu Do ◽  
Pascal Omnes ◽  
Yohan Penel
Keyword(s):  
Wave Equation ◽  
Source Term ◽  
Linear Wave ◽  
Linear Wave Equation

scholarly journals Radial solutions to the Cauchy problem for □1+3U = 0 as limits of exterior solutions

2016 ◽  
Vol 13 (04) ◽  
pp. 833-860
Author(s):  
Helge Kristian Jenssen ◽  
Charis Tsikkou
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Cauchy Data ◽  
Linear Wave ◽  
Radial Solutions ◽  
Linear Wave Equation ◽  
Model Situation ◽  
Neumann Solutions

We consider the strategy of realizing the solution of a Cauchy problem (CP) with radial data as a limit of radial solutions to initial-boundary value problems posed on the exterior of vanishing balls centered at the origin. The goal is to gauge the effectiveness of this approach in a simple, concrete setting: the three-dimensional (3d), linear wave equation [Formula: see text] with radial Cauchy data [Formula: see text], [Formula: see text]. We are primarily interested in this as a model situation for other, possibly nonlinear, equations where neither formulae nor abstract existence results are available for the radial symmetric CP. In treating the 3d wave equation, we therefore insist on robust arguments based on energy methods and strong convergence. (In particular, this work does not address what can be established via solution formulae.) Our findings for the 3d wave equation show that while one can obtain existence of radial Cauchy solutions via exterior solutions, one should not expect such results to be optimal. The standard existence result for the linear wave equation guarantees a unique solution in [Formula: see text] whenever [Formula: see text]. However, within the constrained framework outlined above, we obtain strictly lower regularity for solutions obtained as limits of exterior solutions. We also show that external Neumann solutions yield better regularity than external Dirichlet solutions. Specifically, for Cauchy data in [Formula: see text], we obtain [Formula: see text]-solutions via exterior Neumann solutions, and only [Formula: see text]-solutions via exterior Dirichlet solutions.

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