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On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems

Carlos Parés, Manuel Castro (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys.102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced...

On the well-posedness and regularity of the wave equation with variable coefficients

Bao-Zhu Guo, Zhi-Xiong Zhang (2007)

ESAIM: Control, Optimisation and Calculus of Variations

An open-loop system of a multidimensional wave equation with variable coefficients, partial boundary Dirichlet control and collocated observation is considered. It is shown that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. The Riemannian geometry method is used in the proof of regularity and the feedthrough operator is explicitly computed.

On time optimal control of the wave equation, its regularization and optimality system

Karl Kunisch, Daniel Wachsmuth (2013)

ESAIM: Control, Optimisation and Calculus of Variations

An approximation procedure for time optimal control problems for the linear wave equation is analyzed. Its asymptotic behavior is investigated and an optimality system including the maximum principle and the transversality conditions for the regularized and unregularized problems are derived.

Ondes soniques

G. Métivier (1987/1988)

Séminaire Équations aux dérivées partielles (Polytechnique)

Opérateurs hyperboliques à caractéristiques de multiplicité constante

Jacques Chazarain (1974)

Annales de l'institut Fourier

Soit P un opérateur hyperbolique à caractéristiques de multiplicité constante. On sait que le problème de Cauchy est mal posé si on n’impose pas une condition, dite de Lévi, sur les termes d’ordre inférieur. On démontre que cette condition implique la possibilité de construire une paramétrix du problème de Cauchy au moyen des opérateurs intégraux de Fourier. On en déduit la résolubilité du problème de Cauchy dans les fonctions C ∞ et dans les espaces de Sobolev.

Operational Methods in the Environment of a Computer Algebra System

Spiridonova, Margarita (2009)

Serdica Journal of Computing

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.The presented research is related to the operational calculus approach and its representative applications. Operational methods are considered, as well as their...

Optical leptons.

Kovachev, Lubomir M. (2004)

International Journal of Mathematics and Mathematical Sciences

Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation

George Avalos, Irena Lasiecka (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The null controllability problem for a structurally damped abstract wave equation –often referred to in the literature as a structurally damped equation– is considered with a view towards obtaining optimal rates of blowup for the associated minimal energy function ℰ min ( T ) , as terminal time T ↓ 0 . Key use is made of the underlying analyticity of the semigroup generated by the elastic operator 𝒜 , as well as of the explicit characterization of its domain of definition. We ultimately find that the blowup rate...

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