The Global Attractors for the Periodic Initial Value Problem For a Coupled Non-linear Wave Equation

1996 ◽  
Vol 19 (2) ◽  
pp. 131-144 ◽  
Author(s):  
Guo Boling ◽  
Yang Linge
Keyword(s):  
Wave Equation ◽  
Initial Value Problem ◽  
Global Attractors ◽  
Linear Wave ◽  
Initial Value ◽  
Linear Wave Equation ◽  
Non Linear

Global well-posedness and linearization of a semilinear 2D wave equation with exponential type nonlinearity

2010 ◽  
Vol 17 (3) ◽  
pp. 543-562 ◽  
Author(s):  
Olfa Mahouachi ◽  
Tarek Saanouni
Keyword(s):  
Wave Equation ◽  
Exponential Type ◽  
Initial Value Problem ◽  
Energy Estimate ◽  
Linear Wave ◽  
Well Posedness ◽  
Two Dimensional ◽  
Initial Value ◽  
Linear Wave Equation ◽  
Funct Anal

Abstract We consider the initial value problem for a two-dimensional semi-linear wave equation with exponential type nonlinearity. We obtain global well-posedness in the energy space. We also establish the linearization of bounded energy solutions in the spirit of Gérard [J. Funct. Anal. 141: 60–98, 1996]. The proof uses Moser–Trudinger type inequalities and the energy estimate.

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