162 research outputs found
A new minimizing-movements scheme for curves of maximal slope
Curves of maximal slope are a reference gradient-evolution notion in metric
spaces and arise as variational formulation of a vast class of nonlinear
diffusion equations. Existence theories for curves of maximal slope are often
based on minimizing-movements schemes, most notably on the Euler scheme. We
present here an alternative minimizing-movements approach, yielding more
regular discretizations, serving as a-posteriori convergence estimator, and
allowing for a simple convergence proof.Comment: 28 pages, 2 figure
Well-posedness and long-time behavior for a class of doubly nonlinear equations
This paper addresses a doubly nonlinear parabolic inclusion of the form
. Existence of a solution is proved under suitable
monotonicity, coercivity, and structure assumptions on the operators and
, which in particular are both supposed to be subdifferentials of
functionals on . Moreover, under additional hypotheses on ,
uniqueness of the solution is proved. Finally, a characterization of
-limit sets of solutions is given and we investigate the convergence of
trajectories to limit points
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