### Abstract

This paper discusses the existence and decay of solutions u(t) of the variational inequality of parabolic type: <u^{’}(t) + Au(t) + Bu(t) − f(t), v(t) − u(t)> ≧ 0 for ∀ v ∈ L^{P}([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.

Original language | English |
---|---|

Pages (from-to) | 79-102 |

Number of pages | 24 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 3 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1980 |

Externally published | Yes |

### Fingerprint

### Keywords

- Decay
- Existence
- Nonlinear
- parabolic variational

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

*International Journal of Mathematics and Mathematical Sciences*,

*3*(1), 79-102. https://doi.org/10.1155/S0161171280000063

**Existence and Decay of Solutions of Some Nonlinear Parabolic Variational Inequalities.** / Nakao, Mitsuhiro; Narazaki, Takashi.

Research output: Contribution to journal › Article

*International Journal of Mathematics and Mathematical Sciences*, vol. 3, no. 1, pp. 79-102. https://doi.org/10.1155/S0161171280000063

}

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

UR - http://www.scopus.com/inward/record.url?scp=84914832477&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84914832477&partnerID=8YFLogxK

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 -