Existence of L1-connections between equilibria of a semilinear parabolic equation

Marek Fila, Hiroshi Matano, Peter Poláčik

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9 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)463-491
Number of pages29
JournalJournal of Dynamics and Differential Equations
Volume14
Issue number3
DOIs
StatePublished - 2002

Bibliographical note

Funding 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.

Keywords

  • Blow-up
  • Connecting orbits
  • L-connections
  • Nonlinear heat equation
  • Semilinear parabolic equation
  • Zero number

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