Pseudospectra of the damped wave equation with unbounded damping

Ahmet Arifoski; Petr Siegl

doi:10.1137/18M1221400

Pseudospectra of the damped wave equation with unbounded damping

Ahmet Arifoski, Petr Siegl

School of Mathematics and Physics

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Abstract

We analyze pseudospectra of the generator of the damped waveequation with unbounded damping. We show that the resolvent norm divergesas Re z → −∞. The highly non-normal character of the operator is a robusteffect preserved even when a strong potential is added. Consequently, spectralinstabilities and other related pseudospectral effects are present.

Original language	English
Pages (from-to)	1343–1362
Journal	SIAM Journal on Mathematical Analysis
Volume	52
Issue number	2
DOIs	https://doi.org/10.1137/18M1221400
Publication status	Published - 24 Mar 2020

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Pseudospectra of the damped wave equation with unbounded damping
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Cite this

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AB - We analyze pseudospectra of the generator of the damped waveequation with unbounded damping. We show that the resolvent norm divergesas Re z → −∞. The highly non-normal character of the operator is a robusteffect preserved even when a strong potential is added. Consequently, spectralinstabilities and other related pseudospectral effects are present.

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Pseudospectra of the damped wave equation with unbounded damping

Abstract

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