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A Parabolic Equation with a Mean-Curvature Type Operator

  • Michiel Bertsch
  • Roberta Dal Passo
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 7)

Abstract

The classical mean-curvature operator arises in geometry, and is given by. Mathematically this operator is of particular interest because of its degeneracy for large gradients. The same type of operators arises also in thermodynamical context in the theory of convex free energy functionals, which are asymptotically linear as the gradient tends to infinity [12]; in particular this leads to the parabolic equation u t = Lu [6]. Observe that here u is supposed to be a function, i.e. u is single-valued, in contrast to the geometric origin of the operator L, where one considers surfaces which may correspond very well to multi-valued functions u.

Keywords

Shock Wave Parabolic Equation Entropy Solution Entropy Condition Ground State Solution 
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 Science+Business Media New York 1992

Authors and Affiliations

  • Michiel Bertsch
    • 1
  • Roberta Dal Passo
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Istituto per le Applicazioni del Calcolo (IAC)RomaItaly

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