Remarks on the Well-Posedness of the Nonlinear Cauchy Problem
Langue
en
Article de revue
Ce document a été publié dans
Contemporary mathematics. 2005, vol. 368, p. 337-356
American Mathematical Society
Résumé en anglais
We show that hyperbolicity is a necessary condition for the well posedness of the noncharacteristic Cauchy problem for nonlinear partial differential equations. We give conditions on the initial data which are necessary ...Lire la suite >
We show that hyperbolicity is a necessary condition for the well posedness of the noncharacteristic Cauchy problem for nonlinear partial differential equations. We give conditions on the initial data which are necessary for the existence of solutions and we analyze Hadamard's instabilities in Sobolev spaces. We also show that genuinely nonlinear equations raise new interesting problems.< Réduire
Mots clés en anglais
Cauchy Problem
well posedness
Hadamard's instability
Origine
Importé de halUnités de recherche