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First Concepts on Global Hyperbolic Cauchy Problems

  • Serge Alinhac
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 17)

Abstract

We consider here for simplicity quasilinear hyperbolic systems of the form
$$ Lu = {\partial _t}u + \sum\limits_{j = 1}^n {Aj(u){\partial _j}u + B(u) = 0,B(0) = 0} $$
(1.1)
for x(x1,...xn)∈ Rn,x0=t∈[0,T],u∈ R; N . The coefficients A j t, B are assumed to be real and smooth fucntions of u in an open domain G containing the origin in its interior. All the solutions we consider will be classical (i.e.C1) solutions.

Keywords

Hyperbolic System Functional Method Differential Inequality Euler System Gronwall Lemma 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 1995

Authors and Affiliations

  • Serge Alinhac
    • 1
  1. 1.Département de MathématiquesUniversité de Paris-SudOrsay CedexFrance

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