ETD system

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Tesi etd-07222012-212053


Thesis type
Tesi di dottorato di ricerca
Author
MACH, NGUYET MINH
URN
etd-07222012-212053
Title
Weak solutions to rate-independent systems: Existence and regularity
Settore scientifico disciplinare
MAT/05
Corso di studi
MATEMATICA
Commissione
tutor Prof. Alberti, Giovanni
commissario Prof. Maggi, Francesco
commissario Prof. Focardi, Matteo
Parole chiave
  • regularity
  • rate-independent systems
  • existence
  • weak solutions
Data inizio appello
31/07/2012;
Consultabilità
completa
Riassunto analitico
Weak solutions for rate-independent systems has been considered by many
authors recently. In this thesis, I shall give a careful explanation
(benefits and drawback) of energetic solutions (proposed by Mielke and
Theil in 1999) and BV solutions constructed by vanishing viscosity
(proposed by Mielke, Rossi and Savare in 2012). In the case of convex
energy functional, then classical results show that energetic solutions is
unique and Lipschitz continuous. However, in the case energy functional is
not convex, there is very few results about regularity of energetic
solutions. In this thesis, I prove the SBV and piecewise C^1 regularity
for energetic solution without requiring the convexity of energy
functional. Another topic of this thesis is about another construction of
BV solutions via epsilon-neighborhood method.
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