Smoothing for the Zakharov and Klein--Gordon--Schrödinger Systems on Euclidean Spaces

2017 ◽  
Vol 49 (5) ◽  
pp. 4206-4231 ◽  
Author(s):  
E. Compaan
Keyword(s):  
Euclidean Spaces ◽  
Klein Gordon ◽  
Schrödinger Systems

scholarly journals Asymptotic Behavior of the coupled Klein-Gordon-Schrödinger systems on compact manifolds

2021 ◽  
Author(s):  
César Augusto Bortot ◽  
Thales Maier Souza ◽  
Janaina Zanchetta
Keyword(s):  
Compact Riemannian Manifold ◽  
Unique Continuation ◽  
Smoothing Effect ◽  
Unique Continuation Property ◽  
Boundary Making ◽  
Klein Gordon ◽  
Schrödinger Systems ◽  
Continuation Property ◽  
Schrödinger System ◽  
Stability Results

This paper is concerned with a 2-dimensional Klein-Gordon-Schrödinger system subject to two types of locally distributed damping on a compact Riemannian manifold $\mathcal{M}$ without boundary. Making use of unique continuation property, the observability inequalities, and the smoothing effect due to Aloui, we obtain exponential stability results.

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