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Loss of regularity for the solutions to hyperbolic equations with non‐regular coefficients—an application to Kirchhoff equation
Author(s) -
Hirosawa Fumihiko
Publication year - 2003
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.397
Subject(s) - mathematics , singularity , hyperbolic partial differential equation , mathematical analysis , cauchy problem , initial value problem , cauchy distribution , partial differential equation
We consider the Cauchy problem for second‐order strictly hyperbolic equations with time‐depending non‐regular coefficients. There is a possibility that singular coefficients make a regularity loss for the solution. The main purpose of this paper is to derive an optimal singularity for the coefficient that the Cauchy problem is C ∞ well‐posed. Moreover, we will apply such a result to the estimate of the existence time of the solution for Kirchhoff equation. Copyright © 2003 John Wiley & Sons, Ltd.