Results 71 to 80 of about 4,144 (169)

The Metivier inequality and ultradifferentiable hypoellipticity

Mathematische Nachrichten, Volume 297, Issue 7, Page 2517-2531, July 2024.
Abstract In 1980, Métivier characterized the analytic (and Gevrey) hypoellipticity of L2$L^2$‐solvable partial linear differential operators by a priori estimates. In this note, we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy–Carleman classes given by suitable weight sequences. We also discuss the case when
Paulo D. Cordaro, Stefan Fürdös
wiley   +1 more source

Null controllability of a model in population dynamics

Electronic Journal of Differential Equations, 2014
In this article, we study the null controllability of a linear model with degenerate diffusion in population dynamics. We develop first a Carleman type inequality for the adjoint system of an intermediate model, and then an observability inequality.
Younes Echarroudi, Lahcen Maniar
doaj  

Shift invariant subspaces in growth spaces and sets of finite entropy

Journal of the London Mathematical Society, Volume 109, Issue 5, May 2024.
Abstract We investigate shift invariant subspaces within the realm of analytic functions in the unit disc, whose radial growth is determined by a majorant w$w$. Our main result offers a complete characterization of the shift invariant subspaces generated by Nevanlinna class functions within the aforementioned class of growth spaces.
Adem Limani
wiley   +1 more source

Lipschitz stability for degenerate parabolic systems

Electronic Journal of Differential Equations, 2014
In this article, we study an inverse problem for weakly degenerate coupled parabolic systems with one force. We establish Lipschitz stability for the source term from measurements of one component of the solution at a positive time and on a subset of
Idriss Boutaayamou, Abdelkarim Hajjaj, Lahcen Maniar   +2 more
doaj  

Lipschitz stability for linear parabolic systems with interior degeneracy

Electronic Journal of Differential Equations, 2014
In this article, we study an inverse problem for linear degenerate parabolic systems with one force. We establish Lipschitz stability for the source term from measurements of one component of the solution at a positive time and on a subset of the ...
Idriss Boutaayamou, Genni Fragnelli, Lahcen Maniar   +2 more
doaj  

Stability result for a time dependent potential in a waveguide

, 2012
We consider the operator $H:= \partial_t -\Delta+V$ in 2D or 3D waveguide. With an adapted global Carleman estimate with singular weight functions we give a stability result for the time dependent part of the potential for this particular geometry.
Gaitan, Patricia, Kian, Yavar
core   +1 more source

Null controllability of nonlinear control systems governed by coupled degenerate parabolic equations

Electronic Journal of Differential Equations, 2019
This article concerns the null controllability of a nonlinear control system governed by coupled degenerate parabolic equations. We first establish the Carleman estimate and the observability inequality for solutions to the conjugate problem.
Fengdan Xu, Jingxue Yin, Mingjun Zhou, Qian Zhou   +3 more
doaj  

Resolvent estimates for the Lam�� operator and failure of Carleman estimates

, 2019
To appear in Journal of Fourier Analysis and ...
Kwon, Yehyun, Lee, Sanghyuk, Seo, Ihyeok
openaire   +2 more sources

Stability estimate for an inverse problem for a fractional kinetic equation via a Carleman inequality

Boundary Value Problems
Fractional kinetic equations are used to model complex physical processes, including anomalous diffusion, memory effects, and long-range interactions. In this study, a coefficient inverse problem for a fractional kinetic equation is considered.
İsmet Gölgeleyen, Özlem Kaytmaz, Muhammed Hasdemir   +2 more
doaj   +1 more source

On Carleman estimates with two large parameters [PDF]

Indiana University Mathematics Journal, 2011
We provide a general framework for the analysis and the derivation of Carleman estimates with two large parameters. For an appropriate form of weight functions strong pseudo-convexity conditions are shown to be necessary and sufficient.
openaire   +1 more source