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Stability of the positive Equilibrium Solution for a Class of Quasilinear Diffusion Equations

  • Piero de Mottoni
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Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’analyse Numérique book series (ISNM, volume 38)

Abstract

Asymptotic stability results are proved for the positive equilibrium solution of a generalized Verhulst equation with diffusion. It is shown that the (unique) positive equilibrium solution, whenever it exists, is asymptotically stable in the \(H_{0}^{1}\) norm and globally attractive in the L2 norm.

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Copyright information

© Springer Basel AG 1977

Authors and Affiliations

  • Piero de Mottoni
    • 1
  1. 1.Istituto per le Applicazioni del Calcolo “M. Picone”Consiglio Nazionale delle RicercheRomaAustralia

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