Nonlinear evolution equations generated by subdifferentials with nonlocal constraints

Risei Kano, Yusuke Murase, and Nobuyuki Kenmochi. "Nonlinear evolution equations generated by subdifferentials with nonlocal constraints." Banach Center Publications 86.1 (2009): 175-194. <http://eudml.org/doc/282342>.

@article{RiseiKano2009,
abstract = {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 $\{φ^t(v;·)\}$ 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 $u^\{\prime \}(t) + ∂φ^t(u;u(t)) ∋ f(t)$, 0 < t < T, in H. Our objective is to discuss the existence question for the associated Cauchy problem.},
author = {Risei Kano, Yusuke Murase, Nobuyuki Kenmochi},
journal = {Banach Center Publications},
keywords = {parabolic quasi-variational inequality},
language = {eng},
number = {1},
pages = {175-194},
title = {Nonlinear evolution equations generated by subdifferentials with nonlocal constraints},
url = {http://eudml.org/doc/282342},
volume = {86},
year = {2009},
}

TY - JOUR
AU - Risei Kano
AU - Yusuke Murase
AU - Nobuyuki Kenmochi
TI - Nonlinear evolution equations generated by subdifferentials with nonlocal constraints
JO - Banach Center Publications
PY - 2009
VL - 86
IS - 1
SP - 175
EP - 194
AB - 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 ${φ^t(v;·)}$ 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 $u^{\prime }(t) + ∂φ^t(u;u(t)) ∋ f(t)$, 0 < t < T, in H. Our objective is to discuss the existence question for the associated Cauchy problem.
LA - eng
KW - parabolic quasi-variational inequality
UR - http://eudml.org/doc/282342
ER -