Numerical solution of a coupled modified Korteweg–de Vries equation by the Galerkin method using quadratic B-splines

2013 ◽  
Vol 90 (11) ◽  
pp. 2353-2371 ◽  
Author(s):  
S. Kutluay ◽  
Y. Ucar
Keyword(s):  
Galerkin Method ◽  
Numerical Solution ◽  
Vries Equation ◽  
B Splines ◽  
De Vries ◽  
The Galerkin Method

CARLEMAN ESTIMATE AND UNIQUE CONTINUATION PROPERTY FOR THE LINEAR STOCHASTIC KORTEWEG–DE VRIES EQUATION

2014 ◽  
Vol 90 (2) ◽  
pp. 283-294 ◽  
Author(s):  
PENG GAO
Keyword(s):  
Galerkin Method ◽  
Uniqueness Theorem ◽  
Vries Equation ◽  
Unique Continuation ◽  
Carleman Estimate ◽  
Well Posedness ◽  
Unique Continuation Property ◽  
De Vries ◽  
Continuation Property ◽  
The Galerkin Method

AbstractIn this paper, we obtain the well posedness of the linear stochastic Korteweg–de Vries equation by the Galerkin method, and then establish the Carleman estimate, leading to the unique continuation property (UCP) for the linear stochastic Korteweg–de Vries equation. This UCP cannot be obtained from the classical Holmgren uniqueness theorem.

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