We give a necessary and sufficient condition for the existence of L 1-connections between equilibria of a semilinear parabolic equation. By an L1-connection from an equilibrium φ- to an equilibrium φ+ we mean a function u(·, t) which is a classical solution on the interval (-∞, T) for some T ∈ ℝ and blows up at t = T but continues to exist in the space L1 for t ∈ [T, ∞) and satisfies u(·, t) → φ± (in a suitable sense) as t → ± ∞. The main tool in our analysis is the zero number.
Bibliographical noteFunding Information:
All three authors were partially supported by JSPS Grant 4023. M.F. and P.P. were partially supported by VEGA Grant 1/7677/20.
- Connecting orbits
- Nonlinear heat equation
- Semilinear parabolic equation
- Zero number