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Asymptotic behavior of solutions of semilinear heat equations on S1

  • Hiroshi Matano
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 13)

Abstract

We study the dynamical behavior of the initial value problem for the equation u t = u xx + f(u, u x ), xS 1 =R/Z, t > 0. One of our main results states that any C 1-bounded solution approaches either a single periodic solution or a set of equilibria as t → ∞. We also consider the case where the solution blows up in a finite time and prove that under certain conditions on f the blow-up set of any solution with nonconstant initial data is a finite set.

Keywords

Parabolic Equation Equilibrium Solution Neumann Boundary Condition Linear Parabolic Equation Liapunov 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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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Hiroshi Matano
    • 1
  1. 1.Department of MathematicsHiroshima UniversityHiroshima 730Japan

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