On exponential decay rate of semigroup associated with second order linear differential equation in Hilbert space with strong damping operator

Nikita V. Artamonov

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arXiv · 1110.0167

On exponential decay rate of semigroup associated with second order linear differential equation in Hilbert space with strong damping operator

Nikita V. Artamonov

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Abstract

We obtain estimate of the exponential decay rate of semigroup associated with second order linear differential equation $u"+Du'+Au=0$ in Hilbert space. We assume that $A$ is a selfadjoint positive definite operator, $D$ is an accretive sectorial operator and $\Ree D\geqδA$, $δ>0$. We obtain a location of the spectrum of a pencil associated with linear differential equation.

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BibTeX RIS

Nikita V. Artamonov. 2011-10-02. On exponential decay rate of semigroup associated with second order linear differential equation in Hilbert space with strong damping operator. https://arxiv.org/abs/1110.0167

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