DOUBLY NONLINEAR EQUATIONS AS CONVEX MINIMIZATION

作者：Akagi Goro^*; Stefanelli Ulisse

来源：SIAM Journal on Mathematical Analysis, 2014, 46(3): 1922-1945.

DOI：10.1137/13091909X

• doubly nonlinear equations
• convex minimization
• duality

We present a variational reformulation of a class of doubly nonlinear parabolic equations as (limits of) constrained convex minimization problems. In particular, an e-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 epsilon -> 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.

• 出版日期2014