Abstract
We give a necessary and sufficient condition for the existence of L 1-connections between equilibria of a semilinear parabolic equation. By an L 1-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 ∈ ∝ and blows up at t = T but continues to exist in the space L 1 for t ∈ [T, ∞) and satisfies u(⋅, t) → φ ± (in a suitable sense) as t → ±∞. The main tool in our analysis is the zero number.
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Fila, M., Matano, H. & Poláčik, P. Existence of L 1-Connections Between Equilibria of a Semilinear Parabolic Equation. Journal of Dynamics and Differential Equations 14, 463–491 (2002). https://doi.org/10.1023/A:1016507330323
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DOI: https://doi.org/10.1023/A:1016507330323