Importance of Boundary Conditions in the Numerical Treatment of Hyperbolic Equations

1969 ◽  
Vol 12 (12) ◽  
pp. II-13 ◽  
Author(s):  
Gino Moretti
Keyword(s):  
Boundary Conditions ◽  
Hyperbolic Equations ◽  
Numerical Treatment

Local state observation for stochastic hyperbolic equations

2020 ◽  
Vol 26 ◽  
pp. 79
Author(s):  
Qi Lü ◽  
Zhongqi Yin
Keyword(s):  
Boundary Conditions ◽  
Hyperbolic Equations ◽  
Unique Continuation ◽  
Local State ◽  
Carleman Estimate ◽  
State Observation ◽  
Unique Continuation Property ◽  
Continuation Property ◽  
Global Carleman Estimate

In this paper, we solve a local state observation problem for stochastic hyperbolic equations without boundary conditions, which is reduced to a local unique continuation property for these equations. This result is proved by a global Carleman estimate. As far as we know, this is the first result in this topic.

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