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Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation

Nikolay Tzvetkov, Nicola Visciglia (2013)

Annales scientifiques de l'École Normale Supérieure

Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.

Gehring theory for time-discrete hyperbolic differential equations

Keisuke Hoshino, Norio Kikuchi (1998)

Commentationes Mathematicae Universitatis Carolinae

This paper is concerned with extending Gehring theory to be applicable to Rothe's approximate solutions to hyperbolic differential equations.

Generalized characteristics uniqueness and regularity of solutions in a hyperbolic system of conservation laws

C. M. Dafermos, X. Geng (1991)

Annales de l'I.H.P. Analyse non linéaire

Generalized Function Algebras and PDEs with Singularities. A Survey.

Marko Nedeljkov, Stevan Pilipović (2006)

Zbornik Radova

Generalized Gevrey classes and multi-quasi-hyperbolic operators.

Calvo, D. (2002)

Rendiconti del Seminario Matematico

Generalized method of lines for first order partial functional differential equations

W. Czernous (2006)

Annales Polonici Mathematici

Classical solutions of initial boundary value problems are approximated by solutions of associated differential difference problems. A method of lines for an unknown function for the original problem and for its partial derivatives with respect to spatial variables is constructed. A complete convergence analysis for the method is given. A stability result is proved by using differential inequalities with nonlinear estimates of the Perron type for the given operators. A discretization...

Generalized n-dimensional Gronwall's inequality and its applications to non-selfadjoint and non-linear hyperbolic equations

Sudhanshu K. Ghoshal, Abha Ghoshal, M. Abu-Masood (1977)

Annales Polonici Mathematici

Generalized periodic solutions of nonlinear telegraph equations (Preliminary communication)

Svatopluk Fučík, Jean Mawhin (1977)

Commentationes Mathematicae Universitatis Carolinae

Generalized Solution to a Semilinear Hyperbolic System with a Non-Lipshitz Nonlinearity.

M. Nedeljkov, Stevan Pilipovic (1998)

Monatshefte für Mathematik

Generalized solutions describing singularity interaction.

Danilov, V.G. (2002)

International Journal of Mathematics and Mathematical Sciences

Generalized solutions of mixed problems for quasilinear hyperbolic systems of functional partial differential equations in the Schauder canonic form

Jan Turo (1989)

Annales Polonici Mathematici

Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations

Tomasz Człapiński (1992)

Annales Polonici Mathematici

Generalized solutions to quasilinear hyperbolic systems in the second canonical form are investigated. A theorem on existence, uniqueness and continuous dependence upon the boundary data is given. The proof is based on the methods due to L. Cesari and P. Bassanini for systems which are not functional.

Generalized Solutions to Semilinear Hyperbolic Systems.

Michael Oberguggenberger (1987)

Monatshefte für Mathematik

Generalized solutions to singular initial-boundary hyperbolic problems with non-lipshitz nonlinearities

Irina Kmit (2006)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

Generalized Stability of Difference Method for Nonlinear Initial Value Problems and its Application

Guo Ben-Yu (1992)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Generalized Strichartz Inequalities for the Wave Equation on the Laguerre Hypergroup

Assal, Miloud, Ben Abdallah, Hacen (2004)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 42B35, 35L35, 35K35In this paper we study generalized Strichartz inequalities for the wave equation on the Laguerre hypergroup using generalized homogeneous Besov-Laguerre type spaces.

Generators of hyperbolic heat equation in nonlinear thermoelasticity

Tommaso Ruggeri (1982)

Rendiconti del Seminario Matematico della Università di Padova

Generic properties of generalized hyperbolic partial differential equations

Dariusz Bielawski (1994)

Annales Polonici Mathematici

The existence and uniqueness of solutions and convergence of successive approximations are considered as generic properties for generalized hyperbolic partial differential equations with unbounded right-hand sides.

Genuinely multi-dimensional non-dissipative finite-volume schemes for transport

Bruno Després, Frédéric Lagoutière (2007)

International Journal of Applied Mathematics and Computer Science

We develop a new multidimensional finite-volume algorithm for transport equations. This algorithm is both stable and non-dissipative. It is based on a reconstruction of the discrete solution inside each cell at every time step. The proposed reconstruction, which is genuinely multidimensional, allows recovering sharp profiles in both the direction of the transport velocity and the transverse direction. It constitutes an extension of the one-dimensional reconstructions analyzed in (Lagoutière, 2005;...

Geometric optics expansions with amplification for hyperbolic boundary value problems: Linear problems

Jean-François Coulombel, Olivier Guès (2010)

Annales de l’institut Fourier

We compute and justify rigorous geometric optics expansions for linear hyperbolic boundary value problems that do not satisfy the uniform Lopatinskii condition. We exhibit an amplification phenomenon for the reflection of small high frequency oscillations at the boundary. Our analysis has two important consequences for such hyperbolic boundary value problems. Firstly, we make precise the optimal energy estimate in Sobolev spaces showing that losses of derivatives must occur from the source terms...

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