Linear Evolution Equations

Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 115)

Abstract

Here we study linear PDE for which one poses an initial-value problem, also called a “Cauchy problem,” say at time t=t 0. The emphasis is on the wave and heat equations:
$$\frac{{\partial }^{2}u} {\partial {t}^{2}} -\Delta u = 0,\quad\frac{\partial u} {\partial t} -\Delta u = 0,$$
(0.1)
though some other sorts of PDE, such as symmetric hyperbolic systems, are also discussed.

Keywords

Manifold Fold Type 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA

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