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Annali di Matematica Pura ed Applicata

, Volume 115, Issue 1, pp 295–310 | Cite as

Stability results for a class of non-linear parabolic equations

  • P. de Mottoni
  • G. Talenti
  • A. Tesei
Article

Summary

We study the asymptotic behaviour of the solutions of the equation ut=Au+λu−|u|αu. Denoting by λ0 the principal eigenvalue of the second-order differential operator A, we shall prove that if λ ⩽ λ0 the only equilibrium solution, namely zero, is asymptotically stable, whereas, if λ>λ0, the nontrivial equilibrium solutions without internal zeros are asymptotically stable. Attractivity and stability are proved both in the L2-norm and in the H 0 1 -norm.

Keywords

Asymptotic Behaviour Differential Operator Parabolic Equation Equilibrium Solution Principal Eigenvalue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1977

Authors and Affiliations

  • P. de Mottoni
    • 1
  • G. Talenti
    • 2
  • A. Tesei
    • 3
  1. 1.Roma
  2. 2.Firenze
  3. 3.Roma

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