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Semilinear Parabolic Systems Under Nonlinear Boundary Conditions

  • Herbert Amann
Conference paper
Part of the NATO ASI Series book series (volume 37)

Abstract

We study problems of the form
$$ u + Au = F(u),\quad Bu = G(u),\quad u(0) = u_o , $$
(A)
which can be considered as abstract counterparts to semilinear parabolic systems under nonlinear boundary conditions.

Keywords

Nonlinear Boundary Condition Follow Diagram Commute Bounded Smooth Domain Linear Boundary Condition Arbitrary Smooth Function 
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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References

  1. [1]
    Amann, H: Semigroups and Nonlinear Evolution Equations. Linear Algebra S Appl. in press.Google Scholar
  2. [2]
    Amann, H: Parabolic Evolution Equations and Nonlinear Boundary Conditions. to appear.Google Scholar
  3. [3]
    Friedman, A. and McLeod, B: Blow-up of Positive Solutions of Semilinear Heat Equations. Ind. Univ. Math. J. 34 (1985), 425–447.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Henry, D: Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. #840, Springer-Verlag, Berlin, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Herbert Amann
    • 1
  1. 1.Mathematisches InstitutUniversität ZürichZürichSchweiz

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