Loss of regularity for the solutions to hyperbolic equations with non‐regular coefficients—an application to Kirchhoff equation | Zendy

Hirosawa Fumihiko | Zendy

Premium

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.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research