#### Title

A Note on the Strong Convergence of Solutions to a Second Order Evolution Equation

#### Publication Date

1-1-2013

#### Document Type

Article

#### Abstract

In this note, with suitable assumptions on p(t) and r(t), we establish the strong convergence of solutions to the following nonlinear second order evolution equation p(t)u ′′(t) + r(t)u ′ (t) ∈ Au(t), a. e. on R + , u(0) = u0, sup t≥0 |u(t)| < +∞, to a zero of A, without assuming A −1 (0) ̸= ∅, and determine the rate of convergence, where A is a general maximal monotone operator. We present also some applications of our result.

COinS

## Comments

Djafari Rouhani B, Khatibzadeh H. A note on the strong convergence of solutions to a second order evolution equation. Journal of Mathematical Analysis and Applications 2013 15 May 2013;401(2):963-6.