### Abstract

We consider the wave equation with viscous damping. The equation is said to be critically damped when the damping is that value for which the spectral abscissa of the associated wave operator is minimized within the class of constant dampings. The critically damped wave operator possesses a nonsemisimple eigenvalue. We present a detailed study of the splitting of this eigenvalue under bounded perturbations of the damping and subsequently show that the critical choice is a local minimizer of the spectral abscissa over lines in the class of all bounded dampmgs.

Original language | English (US) |
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Pages (from-to) | 1353-1362 |

Number of pages | 10 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 56 |

Issue number | 5 |

State | Published - Oct 1996 |

### Fingerprint

### Keywords

- Multiple eigenvalue
- Nonselfadjoint operator
- Spectral abscissa

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*56*(5), 1353-1362.

**Perturbing the critically damped wave equation.** / Cox, Steven J.; Overton, Michael L.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 56, no. 5, pp. 1353-1362.

}

TY - JOUR

T1 - Perturbing the critically damped wave equation

AU - Cox, Steven J.

AU - Overton, Michael L.

PY - 1996/10

Y1 - 1996/10

N2 - We consider the wave equation with viscous damping. The equation is said to be critically damped when the damping is that value for which the spectral abscissa of the associated wave operator is minimized within the class of constant dampings. The critically damped wave operator possesses a nonsemisimple eigenvalue. We present a detailed study of the splitting of this eigenvalue under bounded perturbations of the damping and subsequently show that the critical choice is a local minimizer of the spectral abscissa over lines in the class of all bounded dampmgs.

AB - We consider the wave equation with viscous damping. The equation is said to be critically damped when the damping is that value for which the spectral abscissa of the associated wave operator is minimized within the class of constant dampings. The critically damped wave operator possesses a nonsemisimple eigenvalue. We present a detailed study of the splitting of this eigenvalue under bounded perturbations of the damping and subsequently show that the critical choice is a local minimizer of the spectral abscissa over lines in the class of all bounded dampmgs.

KW - Multiple eigenvalue

KW - Nonselfadjoint operator

KW - Spectral abscissa

UR - http://www.scopus.com/inward/record.url?scp=0030269056&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030269056&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030269056

VL - 56

SP - 1353

EP - 1362

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 5

ER -