Well-posedness and unique continuation property for the generalized Ostrovsky equation with low regularity

2015 ◽  
Vol 39 (10) ◽  
pp. 2488-2513 ◽  
Author(s):  
Zaiyun Zhang ◽  
Jianhua Huang
Keyword(s):  
Unique Continuation ◽  
Well Posedness ◽  
Low Regularity ◽  
Unique Continuation Property ◽  
Ostrovsky Equation ◽  
Continuation Property

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.

scholarly journals Strict monotonicity and unique continuation of the biharmonic operator - doi: 10.5269/bspm.v30i2.14502

1970 ◽  
Vol 30 (2) ◽  
pp. 79-83
Author(s):  
Najib Tsouli ◽  
Omar Chakrone ◽  
Mostafa Rahmani ◽  
Omar Darhouche
Keyword(s):  
Unique Continuation ◽  
Biharmonic Operator ◽  
Strict Monotonicity ◽  
Unique Continuation Property ◽  
Continuation Property

In this paper, we will show that the strict monotonicity of the eigenvalues of the biharmonic operator holds if and only if some unique continuation property is satisfied by the corresponding eigenfunctions.

scholarly journals Unique continuation for non-negative solutions of quasilinear elliptic equations

2001 ◽  
Vol 64 (1) ◽  
pp. 149-156 ◽  
Author(s):  
Pietro Zamboni
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Unique Continuation ◽  
Quasilinear Elliptic Equations ◽  
Kato Class ◽  
Unique Continuation Property ◽  
Continuation Property ◽  
Quasilinear Elliptic

Dedicated to Filippo ChiarenzaThe aim of this note is to prove the unique continuation property for non-negative solutions of the quasilinear elliptic equation We allow the coefficients to belong to a generalized Kato class.

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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