Nonlinear Parabolic Equations

Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 117)

Abstract

We begin this chapter with some general results on the existence and regularity of solutions to semilinear parabolic PDE, first treating the pure initial-value problem in § 1, for PDE of the form
$$\frac{\partial u} {\partial t} = Lu + F(t,x,u,\nabla u),\quad u(0) = f,$$
(0.1)
where u is defined on [0, T) ×M, and M has no boundary. Some of the results established in § 1 will be useful in the next chapter, on nonlinear, hyperbolic equations. We also give a precursor to results on the global existence of weak solutions, which will be examined further in Chap. 17, in the context of the Navier–Stokes equations for fluids.

Keywords

Manifold Nash Mos3 Mos2 

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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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