# On the convergence of attractors and exponential attractors for singularly perturbed hyperbolic equations

A. Eden, A. Milani

Research output: Contribution to journalArticle

3 Citations (Scopus)

### Abstract

This paper studies the dynamical behavior of parabolic equations under singular hyperbolic perturbations. In particular it is shown that for damped semilinear hyperbolic equations that are obtained as a singular perturbation of a parabolic equation, a finite dimensional global attractor exists and as the perturbation parameter tends to zero the attractor of the hyperbolic equation converges in some sense to the attractor of the corresponding parabolic partial differential equation. As the most challenging example, the authors treat throughout the paper the case of Klein-Gordon equation in three dimensional space when damping, which is inversely related to the perturbation parameter, is very large. (Authors)

Original language English 102-117 16 Turkish Journal of Mathematics 19 1 Published - Jan 1 1995

### Fingerprint

Exponential Attractors
Parameter Perturbation
Singularly Perturbed
Hyperbolic Equations
Parabolic Equation
Attractor
Klein-Gordon Equation
Semilinear Equations
Parabolic Partial Differential Equations
Global Attractor
Singular Perturbation
Dynamical Behavior
Damped
Damping
Tend
Perturbation
Converge
Three-dimensional
Zero

### All Science Journal Classification (ASJC) codes

• Mathematics(all)

### Cite this

title = "On the convergence of attractors and exponential attractors for singularly perturbed hyperbolic equations",
abstract = "This paper studies the dynamical behavior of parabolic equations under singular hyperbolic perturbations. In particular it is shown that for damped semilinear hyperbolic equations that are obtained as a singular perturbation of a parabolic equation, a finite dimensional global attractor exists and as the perturbation parameter tends to zero the attractor of the hyperbolic equation converges in some sense to the attractor of the corresponding parabolic partial differential equation. As the most challenging example, the authors treat throughout the paper the case of Klein-Gordon equation in three dimensional space when damping, which is inversely related to the perturbation parameter, is very large. (Authors)",
author = "A. Eden and A. Milani",
year = "1995",
month = "1",
day = "1",
language = "English",
volume = "19",
pages = "102--117",
journal = "Turkish Journal of Mathematics",
issn = "1300-0098",
publisher = "TUBITAK",
number = "1",

}

In: Turkish Journal of Mathematics, Vol. 19, No. 1, 01.01.1995, p. 102-117.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the convergence of attractors and exponential attractors for singularly perturbed hyperbolic equations

AU - Eden, A.

AU - Milani, A.

PY - 1995/1/1

Y1 - 1995/1/1

N2 - This paper studies the dynamical behavior of parabolic equations under singular hyperbolic perturbations. In particular it is shown that for damped semilinear hyperbolic equations that are obtained as a singular perturbation of a parabolic equation, a finite dimensional global attractor exists and as the perturbation parameter tends to zero the attractor of the hyperbolic equation converges in some sense to the attractor of the corresponding parabolic partial differential equation. As the most challenging example, the authors treat throughout the paper the case of Klein-Gordon equation in three dimensional space when damping, which is inversely related to the perturbation parameter, is very large. (Authors)

AB - This paper studies the dynamical behavior of parabolic equations under singular hyperbolic perturbations. In particular it is shown that for damped semilinear hyperbolic equations that are obtained as a singular perturbation of a parabolic equation, a finite dimensional global attractor exists and as the perturbation parameter tends to zero the attractor of the hyperbolic equation converges in some sense to the attractor of the corresponding parabolic partial differential equation. As the most challenging example, the authors treat throughout the paper the case of Klein-Gordon equation in three dimensional space when damping, which is inversely related to the perturbation parameter, is very large. (Authors)

UR - http://www.scopus.com/inward/record.url?scp=0029106813&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029106813&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0029106813

VL - 19

SP - 102

EP - 117

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

SN - 1300-0098

IS - 1

ER -
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