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Archive for Rational Mechanics and Analysis

, Volume 117, Issue 4, pp 349–387 | Cite as

Hyperbolic phenomena in a strongly degenerate parabolic equation

  • Michiel Bertsch
  • Roberta Dal Passo
Article

Abstract

We consider the equation u t =(ϕ(u) ψ (u x )) x , where ϕ>0 and where ψ is a strictly increasing function with lims→∞ψ=ψ<∞. We solve the associated Cauchy problem for an increasing initial function, and discuss to what extent the solution behaves qualitatively like solutions of the first-order conservation law u t (ϕ(u)) x . Equations of this type arise, for example, in the theory of phase transitions where the corresponding free-energy functional has a linear growth rate with respect to the gradient.

Keywords

Growth Rate Neural Network Phase Transition Complex System Cauchy Problem 
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

© Springer-Verlag 1992

Authors and Affiliations

  • Michiel Bertsch
    • 1
    • 2
  • Roberta Dal Passo
    • 1
  1. 1.Dipartimento di Matematica IIUniversitá di Roma “Tor Vergata”Rome
  2. 2.Istituto per le Applicazioni del CalcoloRome

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