Differential and Integral Equations

Pullback dynamics of non-autonomous wave equations with acoustic boundary condition

Abstract

This paper is concerned with a class of wave equations with acoustic boundary condition subject to non-autonomous external forces. Under some general assumptions, the problem generates a well-posed evolution process. Then, we establish the existence of a minimal pullback attractor within a universe of tempered sets defined by the forcing terms. We also, study the upper semicontinuity of attractors as the non-autonomous perturbation tends to zero. Our results allow unbounded external forces and nonlinearities with critical growth.

Article information

Source
Differential Integral Equations, Volume 30, Number 5/6 (2017), 443-462.

Dates
First available in Project Euclid: 18 March 2017

https://projecteuclid.org/euclid.die/1489802421

Mathematical Reviews number (MathSciNet)
MR3626583

Zentralblatt MATH identifier
06738556

Citation

Ma, To Fu; Souza, Thales Maier. Pullback dynamics of non-autonomous wave equations with acoustic boundary condition. Differential Integral Equations 30 (2017), no. 5/6, 443--462. https://projecteuclid.org/euclid.die/1489802421