Prolongation of classical solutions and singularities of generalized solutions
Mikio Tsuji
Department of Mathematics, Kyoto Sangyo University, Kamigamo, Kyoto 603, Japan
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Abstract
We consider the Cauchy problem for general partial differential equations of first order. It is well known that it admits locally a smooth solution. When we extend a solution of class , what kinds of phenomena may appear? The aim of this paper is to see what may happen in this extension. Our method depends principally on the analysis of characteristic curves.
Résumé
Nous considérons le problème de Cauchy pour les équations aux dérivées partielles du premier ordre. Nous savons bien qu’il admet localement une solution régulière. Qu’est ce qui se passe quand on prolonge la solution de classe ? Le but de cet article est d’étudier les phénomènes qui apparaissent dans cette extension. Notre méthode dépend principalement de l’analyse des courbes caractéristiques.
Cite this article
Mikio Tsuji, Prolongation of classical solutions and singularities of generalized solutions. Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), no. 6, pp. 505–523
DOI 10.1016/S0294-1449(16)30279-7