scholarly journals Global Carleman estimate for the Kawahara equation and its applications

2018 ◽  
Vol 17 (5) ◽  
pp. 1853-1874 ◽  
Author(s):  
Peng Gao ◽  
Keyword(s):  
Carleman Estimate ◽  
Kawahara Equation ◽  
Global Carleman Estimate

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.

scholarly journals Global Carleman estimate on a network for the wave equation and application to an inverse problem

2011 ◽  
Vol 1 (3) ◽  
pp. 307-330 ◽  
Author(s):  
Lucie Baudouin ◽  
◽  
Emmanuelle Crépeau ◽  
Julie Valein ◽  
◽  
...  
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Carleman Estimate ◽  
Global Carleman Estimate

scholarly journals On the determination of the principal coefficient from boundary measurements in a KdV equation

2014 ◽  
Vol 22 (6) ◽  
Author(s):  
Lucie Baudouin ◽  
Eduardo Cerpa ◽  
Emmanuelle Crépeau ◽  
Alberto Mercado
Keyword(s):  
Inverse Problem ◽  
Kdv Equation ◽  
Carleman Estimate ◽  
Lipschitz Stability ◽  
Single Solution ◽  
De Vries ◽  
Boundary Measurements ◽  
Global Carleman Estimate

AbstractThis paper concerns the inverse problem of retrieving the principal coefficient in a Korteweg–de Vries (KdV) equation from boundary measurements of a single solution. The Lipschitz stability of this inverse problem is obtained using a new global Carleman estimate for the linearized KdV equation. The proof is based on the Bukhgeĭm–Klibanov method.

A NEW UNIQUE CONTINUATION PROPERTY FOR THE KORTEWEG–DE VRIES EQUATION

2014 ◽  
Vol 90 (1) ◽  
pp. 90-98 ◽  
Author(s):  
MO CHEN ◽  
PENG GAO
Keyword(s):  
Vries Equation ◽  
Finite Interval ◽  
Unique Continuation ◽  
Carleman Estimate ◽  
Unique Continuation Property ◽  
De Vries ◽  
Continuation Property ◽  
Global Carleman Estimate

AbstractThe aim of this paper is to obtain a new unique continuation property (UCP) for the Korteweg–de Vries equation posed on a finite interval. Compared with the previous UCP, we need fewer conditions on the solution. For this purpose, we have to establish a global Carleman estimate for the Korteweg–de Vries equation.

scholarly journals Local Exact Controllability to the Trajectories of Burgers–Fisher Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xiaofeng Shi
Keyword(s):  
Linear System ◽  
Exact Controllability ◽  
Second Order ◽  
Carleman Estimate ◽  
Inverse Theory ◽  
Fisher Equation ◽  
Parabolic Operator ◽  
Global Carleman Estimate ◽  
Controllability Result

This paper is addressed to study local exact controllability to the trajectories of the Burgers–Fisher (BF) equation. By using the global Carleman estimate for the second-order parabolic operator, we establish the observable inequality and obtain the exact controllability to the trajectories of the linear system. Then, by local inverse theory, we consider the controllability result for the Burgers–Fisher equation.

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