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)


We consider here for simplicity quasilinear hyperbolic systems of the form
$$ Lu = {\partial _t}u + \sum\limits_{j = 1}^n {Aj(u){\partial _j}u + B(u) = 0,B(0) = 0} $$
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.


Hyperbolic System Functional Method Differential Inequality Euler System Gronwall Lemma 
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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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