Convergence of a Time Discretisation for Doubly Nonlinear Evolution Equations of Second Order

Convergence of a Time Discretisation for Doubly Nonlinear Evolution Equations of Second Order: "

Abstract The convergence of a time discretisation with variable time steps is shown for a class of doubly nonlinear evolution equations
of second order. This also proves existence of a weak solution. The operator acting on the zero-order term is assumed to be
the sum of a linear, bounded, symmetric, strongly positive operator and a nonlinear operator that fulfils a certain growth
and a Hölder-type continuity condition. The operator acting on the first-order time derivative is a nonlinear hemicontinuous
operator that fulfils a certain growth condition and is (up to some shift) monotone and coercive.

• Content Type Journal Article
• DOI 10.1007/s10208-010-9061-5
• Authors
  
  
  • Etienne Emmrich, Universität Bielefeld Fakultät für Mathematik Postfach 100131 33501 Bielefeld Germany
  • Mechthild Thalhammer, Leopold-Franzens-Universität Innsbruck Institut für Mathematik Technikerstraße 13/VII 6020 Innsbruck Austria
  
  

• Journal Foundations of Computational Mathematics
• Online ISSN 1615-3383
• Print ISSN 1615-3375

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