Doubly Nonlinear Evolution Equations as Convex Minimization Problems
نویسنده
چکیده
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 [4] 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.
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