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An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations

Éric Boillat (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we consider the initial value problem which is obtained after a space discretization (with space step h) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size h chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between h and the time...

An improved maximal inequality for 2D fractional order Schrödinger operators

Changxing Miao, Jianwei Yang, Jiqiang Zheng (2015)

Studia Mathematica

The local maximal operator for the Schrödinger operators of order α > 1 is shown to be bounded from H s ( ² ) to L² for any s > 3/8. This improves the previous result of Sjölin on the regularity of solutions to fractional order Schrödinger equations. Our method is inspired by Bourgain’s argument in the case of α = 2. The extension from α = 2 to general α > 1 faces three essential obstacles: the lack of Lee’s reduction lemma, the absence of the algebraic structure of the symbol and the inapplicable...

An improved regularity criteria for the MHD system based on two components of the solution

Zujin Zhang, Yali Zhang (2021)

Applications of Mathematics

As observed by Yamazaki, the third component b 3 of the magnetic field can be estimated by the corresponding component u 3 of the velocity field in L λ ( 2 λ 6 )...

An Ingham type proof for a two-grid observability theorem

Michel Mehrenberger, Paola Loreti (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Here, we prove the uniform observability of a two-grid method for the semi-discretization of the 1 D -wave equation for a time T > 2 2 ; this time, if the observation is made in ( - T / 2 , T / 2 ) , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I 338 (2004) 413–418]. Our proof follows an Ingham type approach.

An Ingham type proof for a two-grid observability theorem

Paola Loreti, Michel Mehrenberger (2007)

ESAIM: Control, Optimisation and Calculus of Variations

Here, we prove the uniform observability of a two-grid method for the semi-discretization of the 1D-wave equation for a time T > 2 2 ; this time, if the observation is made in ( - T / 2 , T / 2 ) , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I338 (2004) 413–418]. Our proof follows an Ingham type approach.

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