Results 211 to 220 of about 9,179 (236)

Unique Continuation Property for the Benjamin Equation

2014
We show that the complex analysis techniques introduced in Bourgain (IMRN Int Math Res Not 9:437–447, 1997) can be used to prove that, if a sufficiently smooth solution to the Benjamin equation is compactly supported in a non trivial time interval then it vanishes identically.
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A NEW UNIQUE CONTINUATION PROPERTY FOR THE KORTEWEG–DE VRIES EQUATION

Bulletin of the Australian Mathematical Society, 2014
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.
Chen, Mo, Gao, Peng
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Unique continuation properties of the nonlinear Schrödinger equation

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1997
Consider the unique continuation problem for the nonlinear Schrödinger (NLS) equationBy using the inverse scattering transform and some results from the Hardy function theory, we prove that if u ∈ C(R; H1(R)) is a solution of the NLS equation, then it cannot have compact support at two different moments unless it vanishes identically.
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Unique Continuation Property for the Coupled Ostrovsky System

Mathematische Nachrichten
ABSTRACT In this paper, we establish a result of unique continuation for the coupled Ostrovsky system that models the evolution of long water waves with small amplitude in the presence of surface tension. More precisely, we will show that if is a solution of the nonlinear system, in a suitable function space, and vanishes on an open
Ricardo Córdoba, Alex M. Montes
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On unique continuation properties for sub-Laplacian on Carnot groups

Acta Mathematica Scientia, 2010
Abstract In this article, authors begin with establishing representation formulas and properties for functions on Carnot groups. Then, some unique continuation results to solutions of sub-Laplace equations with potentials are proved.
Niu Pengcheng, Wang Jialin
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Strong Unique Continuation Properties for Elliptic Operators

2019
In this chapter, we introduce the notion of strong unique continuation for solutions of elliptic equations. Under suitable assumptions on the potential V, a solution of an elliptic differential inequality of type \(\vert {\Delta u}\vert \le \vert {Vu}\vert \) which is flat at a given point should vanish on the connected component of that point.
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Monotonicity properties of variational integrals, \(A_ p\) weights and unique continuation

1986
The paper deals with estimates for the solution of \(div(A(x)\nabla u(x))=0\) (A(x) a Lipschitz, positive definite matrix), and of the Schrödinger equation \(-\Delta u(x)+V(x)u(x)=0.\) The conclusions for the first equation are that \(| u|\) and \(| \nabla u|\) are an \(A_ p\) and an \(A_ q\) ``weight of Muckenhoupt'', respectively, over a ball ...
GAROFALO, NICOLA, F. Lin
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The unique continuation property for second order evolution PDEs

SN Partial Differential Equations and Applications, 2021
Mourad Choulli, Choulli Mourad
exaly  

Unique Continuation Properties for Partial Differential Equations

This book provides a comprehensive and self-contained introduction to the study of the Cauchy problem and unique continuation properties for partial differential equations. Aimed at graduate and advanced undergraduate students, it bridges foundational concepts such as Lebesgue measure theory, functional analysis, and partial differential equations with
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A unique continuation property for the wave equation in a time-dependent domain

Journal of Mathematical Analysis and Applications, 2022
Mitsuhiro Nakao
exaly