### 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 |

### Keywords

- Decay
- Existence
- Nonlinear
- parabolic variational

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

## Fingerprint Dive into the research topics of 'Existence and Decay of Solutions of Some Nonlinear Parabolic Variational Inequalities'. Together they form a unique fingerprint.

## Cite this

Nakao, M., & Narazaki, T. (1980). Existence and Decay of Solutions of Some Nonlinear Parabolic Variational Inequalities.

*International Journal of Mathematics and Mathematical Sciences*,*3*(1), 79-102. https://doi.org/10.1155/S0161171280000063