Hyperbolic Cauchy problem and Leray's residue formula

2000/11/23 by Susumu Tanabé, Tanabé, Susumu
Mathematics · Physics and Astronomy · #35L25 #58G17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Waves and Solitons #math.AG #math.AP #msc:35L25 #msc:58G17

paper · pdf · doi:10.48550/arxiv.math/0011201

14 pages, Talk at the International Banach Mathematical Centre, Warsaw, March 1999

arxiv created 2000/11/23 · openalex publication_date 2000/11/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an algebraic description of wave fronts that appear in strictly hyperbolic Cauchy problem. Concrete form of definig function of wave front issued from initial algebraic variety is obtained by the aid of the Gauss-Manin systems satisfied by Gel'fand -Leray integrals.

Related

• Hyperbolic Formulas in Elliptic Cauchy Problems
• Wave fronts and (almost) free divisors
• Geometric Wave Equations
• First integrals for non linear hyperbolic equations
• Propagators from characteristic surfaces