Semilinear Parabolic Systems Under Nonlinear Boundary Conditions

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


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


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