Results 71 to 80 of about 160 (154)

Conditional stability of a solution of a difference scheme for an ill-posed Cauchy problem

Electronic Journal of Differential Equations, 2018
In this article, we obtain criteria for stability of two-layer difference schemes for an abstract ill-posed Cauchy problem. Method of proof is based on obtaining a priori difference weighted Carleman type estimates.
Murat A. Sultanov, Musabek I. Akylbaev, Raskul Ibragimov   +2 more
doaj  

Null controllability for linear parabolic cascade systems with interior degeneracy

Electronic Journal of Differential Equations, 2016
We study the null controllability problem for linear degenerate parabolic systems with one control force through Carleman estimates for the associated adjoint problem.
Idriss Boutaayamou, Jawad Salhi
doaj  

Uniqueness results for variable coefficient Schrödinger equations

Bruno Pini Mathematical Analysis Seminar
In this note we shall present some result proved in [16] on the uniqueness of Schrödinger equations with space-variable coefficients, that is Schrödinger equations where the Laplacian is replaced by an elliptic operator with space-variable coefficients.
Serena Federico
doaj   +1 more source

Carleman Type Estimates in an Anisotropic Case and Applications

Journal of Differential Equations, 1993
We give proofs and some further applications of estimates announced in the author's note [Sov. Math. Dokl. 22, 639-642 (1980); transl. from Dokl. Akad. Nauk SSSR 255, 18-21 (1980; Zbl 0468.35030)]. These results extend those of \textit{L. Hörmander} [Linear partial differential operators, Springer, Berlin etc.
openaire   +2 more sources

Dynamics-aware Representation Learning via Multivariate Time Series Transformers. [PDF]

Eur Symp Artif Neural Netw Comput Intell Mach Learn, 2022
Potter M, Potter İY, Camps O, Sznaier M.   +3 more
europepmc   +1 more source

Carleman estimates for higher step Grushin operators

Journal of Functional Analysis
The higher step Grushin operators $\Delta_{\alpha}$ are a family of sub-elliptic operators which degenerate on a sub-manifold of $\mathbb{R}^{n+m}$. This paper establishes Carleman-type inequalities for these operators. It is achieved by deriving a weighted $L^{p}-L^{q}$ estimate for the Grushin-harmonic projector.
Hendrik De Bie, Pan Lian
openaire   +2 more sources

Nonlinear Conditions for Ultradifferentiability. [PDF]

J Geom Anal, 2021
Nenning DN, Rainer A, Schindl G.
europepmc   +1 more source

Unique continuation principle for high order equations of Korteweg-de Vries type

Electronic Journal of Differential Equations, 2013
In this article we consider the problem of unique continuation for high-order equations of Korteweg-de Vries type which include the kdV hierarchy.
Pedro Isaza
doaj  

Carleman estimates for geodesic X-ray transforms

Annales Scientifiques de l'École Normale Supérieure
In this article we introduce an approach for studying the geodesic X-ray transform and related geometric inverse problems by using Carleman estimates. The main result states that on compact negatively curved manifolds (resp. nonpositively curved simple or Anosov manifolds), the geodesic vector field satisfies a Carleman estimate with logarithmic ...
Paternain, Gabriel P., Salo, Mikko
openaire   +3 more sources

Exact controllability for systems describing plate vibrations. A perturbation approach

Comptes Rendus. Mathématique
The aim of this paper is to prove new exact controllability properties of systems described by perturbations of the classical Kirchhoff plate equation. We first consider systems described by an abstract plate equation with a bounded control operator. The
Bournissou, Megane, Ervedoza, Sylvain, Tucsnak, Marius   +2 more
doaj   +1 more source