scholarly journals Global solutions of nonlinear wave–Klein–Gordon system in one space dimension

2020 ◽  
Vol 191 ◽  
pp. 111641
Author(s):  
Yue Ma
Keyword(s):  
Nonlinear Wave ◽  
Space Dimension ◽  
Global Solutions ◽  
Klein Gordon ◽  
One Space Dimension

scholarly journals LOW REGULARITY WELL-POSEDNESS OF THE DIRAC–KLEIN–GORDON EQUATIONS IN ONE SPACE DIMENSION

2008 ◽  
Vol 10 (02) ◽  
pp. 181-194 ◽  
Author(s):  
SIGMUND SELBERG ◽  
ACHENEF TESFAHUN
Keyword(s):  
Dirac Operator ◽  
Space Dimension ◽  
One Dimension ◽  
Well Posedness ◽  
Low Regularity ◽  
Klein Gordon ◽  
One Space Dimension

We extend recent results of Machihara and Pecher on low regularity well-posedness of the Dirac–Klein–Gordon (DKG) system in one dimension. Our proof, like that of Pecher, relies on the null structure of DKG, recently completed by D'Ancona, Foschi and Selberg, but we show that in 1d the argument can be simplified by modifying the choice of projections for the Dirac operator. We also show that the result is best possible up to endpoint cases, if one iterates in Bourgain–Klainerman–Machedon spaces.

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.

Convergence of diffusive BGK approximations for nonlinear strongly parabolic systems

2002 ◽  
Vol 132 (2) ◽  
pp. 341-358 ◽  
Author(s):  
Corrado Lattanzio ◽  
Roberto Natalini
Keyword(s):  
Space Dimension ◽  
Global Solutions ◽  
Parabolic Systems ◽  
Compensated Compactness ◽  
Rigorous Result ◽  
Formal Limit ◽  
One Space Dimension

We study a class of BGK approximations of parabolic systems in one space dimension. We prove stability and existence of global solutions for this model. Moreover, under certain conditions, we prove a rigorous result of convergence toward the formal limit, by using compensated compactness techniques.

Sign in / Sign up

Export Citation Format

Share Document