We consider an abstract formulation for a class of parabolic quasi-variational inequalities or quasi-linear PDEs, which are generated by subdifferentials of convex functions with various nonlocal constraints depending on the unknown functions. In this paper we specify a class of convex functions on a real Hilbert space H, with parameters 0 ≤ t ≤ T and v in a set of functions from [-δ₀,T], 0 < δ₀ < ∞, into H, in order to formulate an evolution equation of the form , 0 < t < T, in H. Our objective is to discuss the existence question for the associated Cauchy problem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-11,
author = {Risei Kano and Yusuke Murase and Nobuyuki Kenmochi},
title = {Nonlinear evolution equations generated by subdifferentials with nonlocal constraints},
journal = {Banach Center Publications},
volume = {86},
year = {2009},
pages = {175-194},
zbl = {1178.35224},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-11}
}
Risei Kano; Yusuke Murase; Nobuyuki Kenmochi. Nonlinear evolution equations generated by subdifferentials with nonlocal constraints. Banach Center Publications, Tome 86 (2009) pp. 175-194. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-11/