Generators with a closure relation

DOI10.7153/OAM-08-08zbMATH Open1303.47060arXiv1309.4322OpenAlexW2079400155MaRDI QIDQ5416614

Felix L. Schwenninger, Hans Zwart

Publication date: 14 May 2014

Published in: Operators and Matrices (Search for Journal in Brave)

Abstract: Assume that a block operator of the form $$, acting on the Banach space $X_{1}imes{X}_2$, generates a contraction $C_0$-semigroup. We show that the operator $A_S$ defined by $$ with the natural domain generates a contraction semigroup on $X_1$. Here, $S$ is a boundedly invertible operator for which $epsilonide-S^{-1}$ is dissipative for some $epsilon>0$. With this result the existence and uniqueness of solutions of the heat equation can be derived from the wave equation.

Full work available at URL: https://arxiv.org/abs/1309.4322

zbMATH Keywords

semigroup of operatorsdissipative operatorsemi-inner-productblock operator

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Applications of operator theory to differential and integral equations (47N20) Linear differential equations in abstract spaces (34G10) Linear accretive operators, dissipative operators, etc. (47B44)

Related Items (4)

Building systems from simple hyperbolic ones ⋮ Stability via closure relations with applications to dissipative and port-Hamiltonian systems ⋮ Feedback theory extended for proving generation of contraction semigroups ⋮ Closure operators and generating sets

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