Hyperbolic Systems with Analytic Coefficients : Well-posedness of the Cauchy Problem / by Tatsuo Nishitani.

Format:

Book

Author/Creator:

Nishitani, Tatsuo., Author.

Series:

Lecture Notes in Mathematics, 1617-9692 ; 2097

Language:

English

Subjects (All):

Differential equations.

Mathematical physics.

Differential Equations.

Mathematical Methods in Physics.

Local Subjects:

Differential Equations.

Mathematical Methods in Physics.

Physical Description:

1 online resource (VIII, 237 p.)

Edition:

1st ed. 2014.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2014.

Language Note:

English

Summary:

This monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general necessary conditions for question (B) in terms of minors of the principal symbols. With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contains strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of multiple order has a nondegenerate characteristic of the same order nearby. .

Contents:

Introduction

Necessary conditions for strong hyperbolicity

Two by two systems with two independent variables

Systems with nondegenerate characteristics

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Print version record.

ISBN:

3-319-02273-3