Treffer: Ill-posedness of degenerate dispersive equations
Title:
Ill-posedness of degenerate dispersive equations
Source:
Nonlinearity (Bristol. Print). 25(9):2655-2680
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 31 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Algèbre linéaire numérique, Numerical linear algebra, Equations aux dérivées partielles, problèmes aux valeurs initiales et problèmes aux valeurs limites dépendant du temps, Partial differential equations, initial value problems and time-dependant initial-boundary value problems, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Donnée numérique, Numerical data, Dato numérico, En série, In series, En serie, Equation dégénérée, Degenerate equation, Ecuación degenerada, Equation dérivée partielle, Partial differential equation, Ecuación derivada parcial, Invariance, Invarianza, Physique mathématique, Mathematical physics, Física matemática, Principe invariance, Invariance principle, Principio invarianza, Problème mal posé, Ill posed problem, Problema mal planteado, Simulation numérique, Numerical simulation, Simulación numérica, Support, Soporte, 35XX, 58J70, 65F22, 65F35, 65M99, 65Mxx, 65N99, 65Nxx, Equation dispersion, Solution autosimilaire
Document Type:
Fachzeitschrift
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, Drexel University, 33rd and Market Streets, Philadelphia, PA 19104, United States
School of Mathematics, University of Minnesota, 206 Church St SE, Minneapolis, MN 55455, United States
School of Mathematics, University of Minnesota, 206 Church St SE, Minneapolis, MN 55455, United States
ISSN:
0951-7715
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.26341254
Database:
PASCAL Archive
Weitere Informationen
In this paper we provide numerical and analytical evidence that some degenerate dispersive partial differential equations are ill-posed. Specifically we study the K(2, 2) equation ut = (u2)xxx + (u2)x and the 'degenerate Airy' equation ut = 2uuxxx. For K(2, 2) our results are computational in nature: we conduct a series of numerical simulations which demonstrate that data which is very small in H2 can be of unit size at a fixed time which is independent of the data's size. For the degenerate Airy equation, our results are fully rigorous: we prove the existence of a compactly supported self-similar solution which, when combined with certain scaling invariances, implies ill-posedness (also in H2).