WIAS Preprint No. 832, (2003)

Heteroclinic orbits between rotating waves of semilinear parabolic equation on the circle


  • Fiedler, Bernold
  • Rocha, Carlos
  • Wolfrum, Matthias

2010 Mathematics Subject Classification

  • 35B41 34C29


  • global attractor, heteroclinic orbit, zero number


We investigate heteroclinic orbits between equilibria and rotating waves for scalar semilinear parabolic reaction-advection-diffusion equations with periodic boundary conditions. Using zero number properties of the solutions and the phase shift equivariance of the equation, we establish a necessary and sufficient condition for the existence of a heteroclinic connection between any pair of hyperbolic equilibria or rotating waves.

Appeared in

  • J. Differential Equations, 201 (2004), pp. 99-138

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