TY - JOUR
T1 - Existence and Decay of Solutions of Some Nonlinear Parabolic Variational Inequalities
AU - Nakao, Mitsuhiro
AU - Narazaki, Takashi
PY - 1980
Y1 - 1980
N2 - This paper discusses the existence and decay of solutions u(t) of the variational inequality of parabolic type: ’(t) + Au(t) + Bu(t) − f(t), v(t) − u(t)> ≧ 0 for ∀ v ∈ LP([0,∞);V (p≧2) with v(t) ∈ K a.e. in [0,∞), where K is a closed convex set of a separable uniformly convex Banach space V, A is a nonlinear monotone operator from V to V* and B is a nonlinear operator from Banach space W to W*. V and W are related as V ⊂ W ⊂ H for a Hilbert space H. No monotonicity assumption is made on B.
AB - This paper discusses the existence and decay of solutions u(t) of the variational inequality of parabolic type: ’(t) + Au(t) + Bu(t) − f(t), v(t) − u(t)> ≧ 0 for ∀ v ∈ LP([0,∞);V (p≧2) with v(t) ∈ K a.e. in [0,∞), where K is a closed convex set of a separable uniformly convex Banach space V, A is a nonlinear monotone operator from V to V* and B is a nonlinear operator from Banach space W to W*. V and W are related as V ⊂ W ⊂ H for a Hilbert space H. No monotonicity assumption is made on B.
KW - Decay
KW - Existence
KW - Nonlinear
KW - parabolic variational
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U2 - 10.1155/S0161171280000063
DO - 10.1155/S0161171280000063
M3 - Article
AN - SCOPUS:84914832477
VL - 3
SP - 79
EP - 102
JO - International Journal of Mathematics and Mathematical Sciences
JF - International Journal of Mathematics and Mathematical Sciences
SN - 0161-1712
IS - 1
ER -