Doubly nonlinear equations as convex minimization

Goro Akagi, U. Stefanelli

研究成果: Article査読

23 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1922-1945
ページ数24
ジャーナルSIAM Journal on Mathematical Analysis
46
3
DOI
出版ステータスPublished - 2014
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 計算数学
  • 応用数学

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