N. Lerner: “Carleman Inequalities”

2021 ◽  
Author(s):  
Genni Fragnelli
Keyword(s):  
Carleman Inequalities

Carleman inequalities for the heat equation in singular domains

2010 ◽  
Vol 348 (5-6) ◽  
pp. 277-282 ◽  
Author(s):  
Abdelhakim Belghazi ◽  
Ferroudja Smadhi ◽  
Nawel Zaidi ◽  
Ouahiba Zair
Keyword(s):  
Heat Equation ◽  
Carleman Inequalities ◽  
Singular Domains

Carleman inequalities and inverse problems for the Schrödinger equation

2008 ◽  
Vol 346 (1-2) ◽  
pp. 53-58 ◽  
Author(s):  
Alberto Mercado ◽  
Axel Osses ◽  
Lionel Rosier
Keyword(s):  
Inverse Problems ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Carleman Inequalities

scholarly journals A short proof of backward uniqueness for some geometric evolution equations

2016 ◽  
Vol 27 (12) ◽  
pp. 1650102 ◽  
Author(s):  
Brett Kotschwar
Keyword(s):  
Evolution Equations ◽  
Short Proof ◽  
Direct Proof ◽  
Uniqueness Of Solutions ◽  
Logarithmic Convexity ◽  
Geometric Evolution Equations ◽  
Carleman Inequalities ◽  
Geometric Evolution ◽  
Backward Uniqueness ◽  
Energy Quantity

We present a simple, direct proof of the backward uniqueness of solutions to a class of second-order geometric evolution equations which includes the Ricci and cross-curvature flows. The proof, based on a classical argument of Agmon–Nirenberg, uses the logarithmic convexity of a certain energy quantity in the place of Carleman inequalities. We further demonstrate the applicability of the technique to the [Formula: see text]-curvature flow and other higher-order equations.

SOME CONTROL RESULTS FOR SIMPLIFIED ONE-DIMENSIONAL MODELS OF FLUID-SOLID INTERACTION

2005 ◽  
Vol 15 (05) ◽  
pp. 783-824 ◽  
Author(s):  
ANNA DOUBOVA ◽  
ENRIQUE FERNÁNDEZ-CARA
Keyword(s):  
Fixed Point ◽  
Burgers Equation ◽  
Null Controllability ◽  
Original Model ◽  
Control Analysis ◽  
One Dimensional ◽  
Carleman Inequalities ◽  
Linearized System ◽  
Fluid Solid Interaction ◽  
Observability Estimates

We analyze the null controllability of a one-dimensional nonlinear system which models the interaction of a fluid and a particle. This can be viewed as a first step in the control analysis of fluid-solid systems. The fluid is governed by the Burgers equation and the control is exerted at the boundary points. We present two main results: the global null controllability of a linearized system and the local null controllability of the nonlinear original model. The proofs rely on appropriate global Carleman inequalities, observability estimates and fixed point arguments.

scholarly journals The variable coefficient thin obstacle problem: Carleman inequalities

2016 ◽  
Vol 301 ◽  
pp. 820-866 ◽  
Author(s):  
Herbert Koch ◽  
Angkana Rüland ◽  
Wenhui Shi
Keyword(s):  
Obstacle Problem ◽  
Variable Coefficient ◽  
Carleman Inequalities ◽  
Thin Obstacle
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