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.

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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