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An existence result for an interior electromagnetic casting problem

Mohammed Barkatou, Diaraf Seck, Idrissa Ly (2006)

Open Mathematics

This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C 2. Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.

An Hadamard maximum principle for the biplacian on hyperbolic manifolds

Håkan Hedenmalm (1999)

Journées équations aux dérivées partielles

We prove the existence of a maximum principle for operators of the type Δ ω - 1 Δ , for weights ω with log ω subharmonic. It is associated with certain simply connected subdomains that are produced by a Hele-Shaw flow emanating from a given point in the domain. For constant weight, these are the circular disks in the domain. The principle is equivalent to the following statement. THEOREM. Suppose ω is logarithmically subharmonic on the unit disk, and that the weight times area measure is a reproducing measure...

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.

An L¹-stability and uniqueness result for balance laws with multifunctions: a model from the theory of granular media

Piotr Gwiazda, Agnieszka Świerczewska (2004)

Colloquium Mathematicae

We study the uniqueness and L¹-stability of the Cauchy problem for a 2 × 2 system coming from the theory of granular media [9,10]. We work in a class of weak entropy solutions. The appearance of a multifunction in a source term, given by the Coulomb-Mohr friction law, requires a modification of definition of the weak entropy solution [5,6].

An observability estimate for parabolic equations from a measurable set in time and its applications

Kim Dang Phung, Gengsheng Wang (2013)

Journal of the European Mathematical Society

This paper presents a new observability estimate for parabolic equations in Ω × ( 0 , T ) , where Ω is a convex domain. The observation region is restricted over a product set of an open nonempty subset of Ω and a subset of positive measure in ( 0 , T ) . This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.

Currently displaying 401 – 420 of 667