Doubly nonlinear equations as convex minimization

Goro Akagi, U. Stefanelli

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

We present a variational reformulation of a class of doubly nonlinear parabolic equations as (limits of) constrained convex minimization problems. In particular, an ε-dependent family of weighted energy-dissipation (WED) functionals on entire trajectories is introduced and proved to admit minimizers. These minimizers converge to solutions of the original doubly nonlinear equation as ε → 0. The argument relies on the suitable dualization of the former analysis of [G. Akagi and U. Stefanelli, J. Funct. Anal., 260 (2011), pp. 2541-2578] and results in a considerable extension of the possible application range of the WED functional approach to nonlinear diffusion phenomena, including the Stefan problem and the porous media equation.

Original languageEnglish
Pages (from-to)1922-1945
Number of pages24
JournalSIAM Journal on Mathematical Analysis
Volume46
Issue number3
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Convex minimization
  • Doubly nonlinear equations
  • Duality

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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