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Evolution equations with discontinuous nonlinearities and non-convex constraints

  • A. Marino
  • C. Saccon
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)

Abstract

We consider here some semilinear parabolic problems with discontinuous nonlinearities, possibly subjected to some convex or even non-convex constraint conditions. We can find solutions of such problems following the abstract framework, which we feel quite simple, presented in section 4: the methods described there originated from the ideas proposed in [9], subsequently developed in [13] and [18]. In this setting, expecially in the constrained problems, the “potential ” function f related to each problem plays a very important role (see 4.13)). We point out that in the case of the non convex constraint, which is made up by the intersection of a convex set K and a smooth hypersurface S, a key point is the non tangency between K and S (see (4.14) ), which are studied in propositions (3.2) and (3.3). This fact resembles the situation in the regular setting: a sufficent condition for the intersection of two manyfolds M 1 and M 2 to be a manyfold is the non tangency between M 1 and M 2.

Keywords

Monotone Operator Differential Inclusion Continuous Curve Convex Constraint Smooth Hypersurface 
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 New York 1990

Authors and Affiliations

  • A. Marino
    • 1
  • C. Saccon
    • 1
  1. 1.Dipartimento di MatematicaPisaItaly

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