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Akagi, G. ; Melchionna, S.* ; Stefanelli, U.*

Weighted energy-dissipation approach to doubly nonlinear problems on the half line.

J. evol. equ. 18, 49–74 (2018)
Postprint DOI
Open Access Green
We discuss a variational approach to abstract doubly nonlinear evolution systems defined on the time half line . This relies on the minimization of weighted energy-dissipation (WED) functionals, namely a family of -dependent functionals defined over entire trajectories. We prove WED functionals admit minimizers and that the corresponding Euler-Lagrange system, which is indeed an elliptic-in-time regularization of the original problem, is strongly solvable. Such WED minimizers converge, up to subsequences, to a solution of the doubly nonlinear system as . The analysis relies on a specific estimate on WED minimizers, which is specifically tailored to the unbounded time interval case. In particular, previous results on the bounded time interval are extended and generalized. Applications of the theory to classes of nonlinear PDEs are also presented.
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Publication type Article: Journal article
Document type Scientific Article
Corresponding Author
Keywords Doubly Nonlinear System ; Variational Approach ; Wed Functionals ; Causal Limit; Elliptic Regularization; Variational Principle; Convex Minimization; Evolution-equations; Minimum Principles; Gradient Flows; Trajectories; Functionals; Relaxation; Conjecture
ISSN (print) / ISBN 1424-3199
e-ISSN 1424-3202
Journal Journal of evolution equations
Quellenangaben Volume: 18, Issue: 1, Pages: 49–74 Article Number: , Supplement: ,
Publisher Birkhäuser
Publishing Place Basel [u.a.]
Non-patent literature Publications
Institute(s) Institute of Computational Biology (ICB)