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September 2011 Some well-posed Cauchy problem for second order hyperbolic equations with two independent variables
Ferruccio Colombini, Tatsuo Nishitani, Nicola Orrù, Ludovico Pernazza
Osaka J. Math. 48(3): 645-673 (September 2011).

Abstract

In this paper we discuss the $C^{\infty}$ well-posedness for second order hyperbolic equations $Pu=\partial_{t}^{2}u-a(t,x) \partial_{x}^{2}u=f$ with two independent variables $(t,x)$. Assuming that the $C^{\infty}$ function $a(t,x) \geq 0$ verifies $\partial_{t}^{p}a(0,0)\neq 0$ with some $p$ and that the discriminant $\Delta(x)$ of $a(t,x)$ vanishes of finite order at $x=0$, we prove that the Cauchy problem for $P$ is $C^{\infty}$ well-posed in a neighbourhood of the origin.

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Ferruccio Colombini. Tatsuo Nishitani. Nicola Orrù. Ludovico Pernazza. "Some well-posed Cauchy problem for second order hyperbolic equations with two independent variables." Osaka J. Math. 48 (3) 645 - 673, September 2011.

Information

Published: September 2011
First available in Project Euclid: 26 September 2011

zbMATH: 1244.35082
MathSciNet: MR2837674

Subjects:
Primary: 35L15
Secondary: 35B30 , 35L80

Rights: Copyright © 2011 Osaka University and Osaka City University, Departments of Mathematics

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Vol.48 • No. 3 • September 2011
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