Taiwanese Journal of Mathematics

Attractors for a Class of Kirchhoff Models with $p$-Laplacian and Time Delay

Sun-Hye Park

Full-text: Open access

Abstract

This paper is concerned with a class of Kirchhoff models with time delay and perturbation of $p$-Laplacian type \[ u_{tt}(x,t) + \Delta^2 u(x,t) - \Delta_p u(x,t) - a_0 \Delta u_t(x,t) + a_1 u_t(x,t-\tau) + f(u(x,t)) = g(x), \] where $\Delta_p u = \operatorname{div}(|\nabla u|^{p-2} \nabla u)$ is the usual $p$-Laplacian operator. Many researchers have studied well-posedness and decay rates of energy for these equations without delay effects. But, there are not many studies on attractors for other delayed systems. Thus we establish the existence of global attractors and the finite dimensionality of the attractors by establishing some functionals which are related to the norm of the phase space to our problem.

Article information

Source
Taiwanese J. Math., Volume 23, Number 4 (2019), 883-896.

Dates
Received: 11 September 2017
Revised: 4 October 2018
Accepted: 11 November 2018
First available in Project Euclid: 18 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1563436873

Digital Object Identifier
doi:10.11650/tjm/181105

Mathematical Reviews number (MathSciNet)
MR3982066

Zentralblatt MATH identifier
07088952

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations 35B41: Attractors

Keywords
attractor finite dimensionality time delay Kirchhoff model $p$-Laplacian

Citation

Park, Sun-Hye. Attractors for a Class of Kirchhoff Models with $p$-Laplacian and Time Delay. Taiwanese J. Math. 23 (2019), no. 4, 883--896. doi:10.11650/tjm/181105. https://projecteuclid.org/euclid.twjm/1563436873


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