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On the Cauchy problem for second order strictly hyperbolic equations with non–regular coefficients
Author(s) -
Hirosawa Fumihiko
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310068
Subject(s) - mathematics , singularity , hyperbolic partial differential equation , mathematical analysis , cauchy problem , order (exchange) , wkb approximation , principal part , initial value problem , second order equation , partial differential equation , differential equation , physics , finance , quantum mechanics , economics
In this paper we shall consider some necessary and sufficient conditions for well–posedness of second order hyperbolic equations with non–regular coefficients with respect to time. We will derive some optimal regularities for well–posedness from the intensity of singularity to the coefficients by WKB representation of the solution and some counter examples which are constructed by using ideas of Floquet theory.