scholarly journals Global existence for equivalent nonlinear special scale invariant damped wave equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Sandra Lucente
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Vector Fields ◽  
Wave Equations ◽  
Small Data ◽  
Damped Wave Equation ◽  
Scale Invariant ◽  
Forcing Term ◽  
Time Existence

<p style='text-indent:20px;'>In this paper we give the notion of equivalent damped wave equations. As an application we study global in time existence for the solution of special scale invariant damped wave equation with small data. To gain such results, without radial assumption, we deal with Klainerman vector fields. In particular we can treat some potential behind the forcing term.</p>

A Modified Test Function Method for Damped Wave Equations

2013 ◽  
Vol 13 (4) ◽  
Author(s):  
Marcello D’Abbicco ◽  
Sandra Lucente
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Critical Exponent ◽  
Function Method ◽  
Wave Equations ◽  
Time Dependent ◽  
Small Data ◽  
Test Function ◽  
Test Function Method ◽  
Modified Test

AbstractIn this paper we use a modified test function method to derive nonexistence results for the semilinear wave equation with time-dependent speed and damping. The obtained critical exponent is the same exponent of some recent results on global existence of small data solutions.

scholarly journals Critical exponent of Fujita-type for semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime

2021 ◽  
Author(s):  
Marcelo Ebert ◽  
Jorge Marques
Keyword(s):  
Wave Equation ◽  
Critical Exponent ◽  
Wave Equations ◽  
Small Data ◽  
Semilinear Wave Equations

We consider the nonlinear massless wave equation belonging to some family of the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. We prove the global in time small data solutions for supercritical powers in the case of decelerating expansion universe.

scholarly journals Stabilization of damped waves on spheres and Zoll surfaces of revolution

2018 ◽  
Vol 24 (4) ◽  
pp. 1759-1788
Author(s):  
Hui Zhu
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Indicator Function ◽  
Geometric Control ◽  
Damped Wave Equation ◽  
Surfaces Of Revolution ◽  
Strong Stabilization ◽  
Geometric Objects ◽  
Dimension 2 ◽  
Appl Math

We study the strong stabilization of wave equations on some sphere-like manifolds, with rough damping terms which do not satisfy the geometric control condition posed by Rauch−Taylor [J. Rauch and M. Taylor, Commun. Pure Appl. Math. 28 (1975) 501–523] and Bardos−Lebeau−Rauch [C. Bardos, G. Lebeau and J. Rauch, SIAM J. Control Optimiz. 30 (1992) 1024–1065]. We begin with an unpublished result of G. Lebeau, which states that on 𝕊d, the indicator function of the upper hemisphere strongly stabilizes the damped wave equation, even though the equators, which are geodesics contained in the boundary of the upper hemisphere, do not enter the damping region. Then we extend this result on dimension 2, to Zoll surfaces of revolution, whose geometry is similar to that of 𝕊2. In particular, geometric objects such as the equator, and the hemi-surfaces are well defined. Our result states that the indicator function of the upper hemi-surface strongly stabilizes the damped wave equation, even though the equator, as a geodesic, does not enter the upper hemi-surface either.

scholarly journals PULLBACK AND FORWARD ATTRACTORS FOR A DAMPED WAVE EQUATION WITH DELAYS

2004 ◽  
Vol 04 (03) ◽  
pp. 405-423 ◽  
Author(s):  
T. CARABALLO ◽  
P. E. KLOEDEN ◽  
J. REAL
Keyword(s):  
Wave Equation ◽  
Compact Set ◽  
Damped Wave Equation ◽  
Forcing Term ◽  
Forward Attractor ◽  
Two Parameter

The existence of a pullback (and also a uniform forward) attractor is proved for a damped wave equation containing a delay forcing term which, in particular, covers the models of sine–Gordon type. The result follows from the existence of a compact set which is uniformly attracting for the two-parameter semigroup associated to the model.

scholarly journals Global existence of solutions to degenerate wave equations with dissipative terms

1999 ◽  
Vol 60 (1) ◽  
pp. 1-10
Author(s):  
Mohammed Aassila
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Asymptotic Behaviour ◽  
Wave Equations ◽  
Existence Of Solutions ◽  
Dissipative Term ◽  
Global Existence Of Solutions ◽  
Asymptotic Behaviour Of Solutions ◽  
Dissipative Terms ◽  
Degenerate Wave Equation

In this paper we prove the global existence and study the asymptotic behaviour of solutions to a degenerate wave equation with a nonlinear dissipative term.

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