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)


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.


Parabolic Equation Equilibrium Solution Neumann Boundary Condition Linear Parabolic Equation Liapunov Function 
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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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