Reflection of singularities of solutions to systems of differential equations

1975/07/01 by Michael E. Taylor · 143 citations
Computer Science · Mathematics · Medicine · #Advanced Differential Equations and Dynamical Systems #Algebra over a field #Calculus (dental) #Citation #Computer science #Differential (mechanical device) #Gravitational singularity #Library science #Mathematical analysis #Mathematical economics #Mathematics #Medicine #Numerical methods for differential equations #Physics #Polynomial and algebraic computation #Programming language #Pure mathematics #Reflection (computer programming) #Taylor series

paper · pdf · doi:10.1002/cpa.3160280403

published in Communications on Pure and Applied Mathematics 28(4), 457-478 (Wiley)

openalex publication_date 1975/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

In this paper we shall examine reflection of singularities of solutions of firstorder equations of the form in a region 9 with boundary given by y=O; say 9 = X a9. Here G = G ( y ) = G ( y , x , 0,) is a smooth one-parameter family of pseudo-differential operators of order one on a 9, G (y) E PS( 1); u takes on values in a vector space, @, and G is a k X k matrix of operators, with principal symbol G,(y,x,t), homogeneous of degree one in 5. On the boundary y = 0, a boundary condition is prescribed :

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