The Cauchy problem for properly hyperbolic equations in one space variable-Reference-Cited by-同舟云学术

The Cauchy problem for properly hyperbolic equations in one space variable

Published:2022-09 Issue:03 Volume:19 Page:439-466
ISSN:0219-8916
Container-title:Journal of Hyperbolic Differential Equations
language:en
Short-container-title:J. Hyper. Differential Equations

Author:

Spagnolo Sergio¹,Taglialatela Giovanni²

Affiliation:

1. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

2. Dipartimento di Economia e Finanza, Università di Bari “Aldo Moro”, Largo Abbazia S. Scolastica, 70124 Bari, Italy

Abstract

In this paper, we consider the Cauchy problem for higher-order weakly hyperbolic equations assuming that the principal symbol depends only on one space variable and the characteristic roots [Formula: see text] verify an inequality like [Formula: see text] We prove that the Cauchy problem is well-posed in [Formula: see text] if the operators with frozen coefficients are uniformly hyperbolic in the sense of Gårding.

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219891622500138

Reference29 articles.

1. On the Cauchy problem for some hyperbolic operator with double characteristics

2. A sufficient condition for hyperbolicity of partial differential operators with constant coefficient principal part

3. Linear hyperbolic partial differential equations with constant coefficients

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