Nonlinear Parabolic Equations

  • Michael E. Taylor
Part of the Applied Mathematical Sciences book series (AMS, volume 117)


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
$$\frac{{\partial u}}{{\partial t}} = Lu + F\left( {t,x,u,\nabla u} \right),u\left( 0 \right) = f,$$
, 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 Chapter 17, in the context of the Navier-Stokes equations for fluids.


Banach Space Vector Field Parabolic Equation Travel Wave Solution Harnack Inequality 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Michael E. Taylor
    • 1
  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA

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