TY - JOUR
T1 - Weighted energy-dissipation functionals for doubly nonlinear evolution
AU - Akagi, Goro
AU - Stefanelli, Ulisse
N1 - Funding Information:
✩ The first author gratefully acknowledges the kind hospitality and support of the IMATI-CNR in Pavia, Italy, where this research was initiated, and the partial support of the SIT grant and the Grant-in-Aid for Young Scientists (B) # 19740073, # 22740093, MEXT. The second author is partly supported by FP7-IDEAS-ERC-StG Grant # 200947 (BioSMA). * Corresponding author. E-mail address: g-akagi@shibaura-it.ac.jp (G. Akagi).
PY - 2011/5/1
Y1 - 2011/5/1
N2 - This paper is concerned with the Weighted Energy-Dissipation (WED) functional approach to doubly nonlinear evolutionary problems. This approach consists in minimizing (WED) functionals defined over entire trajectories. We present the features of the WED variational formalism and analyze the related Euler-Lagrange problems. Moreover, we check that minimizers of the WED functionals converge to the corresponding limiting doubly nonlinear evolution. Finally, we present a discussion on the functional convergence of sequences of WED functionals and present some application of the abstract theory to nonlinear PDEs.
AB - This paper is concerned with the Weighted Energy-Dissipation (WED) functional approach to doubly nonlinear evolutionary problems. This approach consists in minimizing (WED) functionals defined over entire trajectories. We present the features of the WED variational formalism and analyze the related Euler-Lagrange problems. Moreover, we check that minimizers of the WED functionals converge to the corresponding limiting doubly nonlinear evolution. Finally, we present a discussion on the functional convergence of sequences of WED functionals and present some application of the abstract theory to nonlinear PDEs.
KW - Doubly nonlinear equations
KW - Variational principle
KW - Γ-convergence
UR - http://www.scopus.com/inward/record.url?scp=79951681433&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79951681433&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2010.12.027
DO - 10.1016/j.jfa.2010.12.027
M3 - Article
AN - SCOPUS:79951681433
VL - 260
SP - 2541
EP - 2578
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 9
ER -