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Delta‐waves for Semilinear Hyperbolic Cauchy Problems
Author(s) -
Oberguggenberger Michael,
Wang YaGuang
Publication year - 1994
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.19941660124
Subject(s) - mathematics , principal part , gravitational singularity , mathematical analysis , hyperbolic partial differential equation , integrable system , space (punctuation) , wave equation , dirac delta function , initial value problem , cauchy problem , constant coefficients , dirac (video compression format) , variable (mathematics) , dirac measure , cauchy distribution , partial differential equation , mathematical physics , dirac equation , philosophy , linguistics , physics , dirac algebra , nuclear physics , neutrino , dirac spinor
This paper deals with the propagation of strong singularities for constant coefficient semilinear hyperbolic equations and systems. Limits of regularized solutions are computed as the initial data converge to derivatives of Dirac measures on lower dimensional submanifolds. A general method is given which applies whenever the fundamental solution to the principal part is an integrable measure. Particular cases are semilinear first order systems in one space variable and the semilinear Klein‐Gordon equation in at most three space variables.