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


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.


Asymptotic Behaviour Differential Operator Parabolic Equation Equilibrium Solution Principal Eigenvalue 
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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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