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Nonlinear Parabolic Operators

  • Alexander Pankov
Chapter
  • 233 Downloads
Part of the Mathematics and Its Applications book series (MAIA, volume 422)

Abstract

Let Q 0R n be a bounded open set and Q = (0, T) × Q 0. On Q, we shall consider evolution operators of the form
$$\angle u = {\partial _t}u - div a(t,x,u,\nabla u) + {a_0}(t,x,u,\nabla u),$$
(4.1.1)
where ∂ t = ∂/∂t. We assume that the functions
$$a:Q \times R \times {R^n} \to {R^n}$$
and
$${a_0}:Q \times R \times {R^n} \to R$$
satisfy the Catathéodory condition and the following inequalities:

Keywords

Unique Solution Weak Solution Reflexive Banach Space Auxiliary Equation Elliptic Case 
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

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Alexander Pankov
    • 1
  1. 1.Vinnitsa Polytechnical InstituteVinnitsaUkraine

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