# Nonlinear evolution equations generated by subdifferentials with nonlocal constraints

Risei Kano; Yusuke Murase; Nobuyuki Kenmochi

Banach Center Publications (2009)

- Volume: 86, Issue: 1, page 175-194
- ISSN: 0137-6934

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topRisei 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 -

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