scholarly journals Existence of a global solution to a semi-linear wave equation with initial data of non-compact support in low space dimensions

1993 ◽  
Vol 22 (2) ◽  
pp. 123-180 ◽  
Author(s):  
Kôji KUBOTA
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Global Solution ◽  
Compact Support ◽  
Linear Wave ◽  
Linear Wave Equation

Estimates for the controls of the wave equation with a potential

2018 ◽  
Vol 24 (1) ◽  
pp. 289-309 ◽  
Author(s):  
Sorin Micu ◽  
Laurenţiu Emanuel Temereancă
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Space Variable ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
One Dimensional ◽  
Boundary Controls ◽  
The One ◽  
Variable Potential ◽  
Uniformly Bounded

This article studies the L2-norm of the boundary controls for the one dimensional linear wave equation with a space variable potential a = a(x). It is known these controls depend on a and their norms may increase exponentially with ||a||L∞. Our aim is to make a deeper study of this dependence in correlation with the properties of the initial data. The main result of the paper shows that the minimal L2−norm controls are uniformly bounded with respect to the potential a, if the initial data have only sufficiently high eigenmodes.

scholarly journals STRICHARTZ ESTIMATES FOR WAVE EQUATION WITH INVERSE SQUARE POTENTIAL

2013 ◽  
Vol 15 (06) ◽  
pp. 1350026 ◽  
Author(s):  
CHANGXING MIAO ◽  
JUNYONG ZHANG ◽  
JIQIANG ZHENG
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Strichartz Estimates ◽  
Linear Wave ◽  
Well Posedness ◽  
Linear Wave Equation ◽  
Admissible Pairs

In this paper, we study the Strichartz-type estimates of the solution for the linear wave equation with inverse square potential. Assuming the initial data possesses additional angular regularity, especially the radial initial data, the range of admissible pairs is improved. As an application, we show the global well-posedness of the semi-linear wave equation with inverse-square potential [Formula: see text] for power p being in some regime when the initial data are radial. This result extends the well-posedness result in Planchon, Stalker, and Tahvildar-Zadeh.

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 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
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