scholarly journals Almost global existence for Hamiltonian semilinear Klein-Gordon equations with small Cauchy data on Zoll manifolds

2007 ◽  
Vol 60 (11) ◽  
pp. 1665-1690 ◽  
Author(s):  
D. Bambusi ◽  
J.-M. Delort ◽  
B. Grébert ◽  
J. Szeftel
Keyword(s):  
Global Existence ◽  
Cauchy Data ◽  
Klein Gordon

scholarly journals Global existence of small amplitude solutions to one-dimensional nonlinear Klein–Gordon systems with different masses

2015 ◽  
Vol 12 (04) ◽  
pp. 745-762 ◽  
Author(s):  
Donghyun Kim
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Small Amplitude ◽  
Space Dimension ◽  
Structural Condition ◽  
Cauchy Data ◽  
One Dimensional ◽  
Compactly Supported ◽  
The Cauchy Problem ◽  
Klein Gordon

We study the Cauchy problem for systems of cubic nonlinear Klein–Gordon equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the rate [Formula: see text] in [Formula: see text], [Formula: see text] as [Formula: see text] tends to infinity even in the case of mass resonance, if the Cauchy data are sufficiently small, smooth and compactly supported.

scholarly journals Global Existence of Maxwell Klein Gordon Theory with General Couplings

2019 ◽  
Vol 1245 ◽  
pp. 012078
Author(s):  
Mulyanto ◽  
F T Akbar ◽  
B E Gunara
Keyword(s):  
Global Existence ◽  
Klein Gordon

Global solutions of quasilinear wave-Klein–Gordon system in two-space dimension: Completion of the proof

2017 ◽  
Vol 14 (04) ◽  
pp. 627-670 ◽  
Author(s):  
Yue Ma
Keyword(s):  
Global Existence ◽  
Space Dimension ◽  
Global Solutions ◽  
Space Time ◽  
Time Dimension ◽  
Regular Solutions ◽  
Complete Proof ◽  
Klein Gordon

Based on the first part, we give a complete proof of the global existence of small regular solutions to a type of quasilinear wave-Klein–Gordon system with null couplings in [Formula: see text] space-time dimension.

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