Solvability and spectral analysis of integro-differential equations arising in the theory of heat transfer and acoustics

DOI10.1134/S1064562410050029zbMath1228.45020MaRDI QIDQ630225

N. A. Rautian, V. V. Vlasov, Alexei S. Shamaev

Publication date: 17 March 2011

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

Laplace transformintegro-differential equationsasymptotic behaviorHilbert spaceweighted Sobolev spacesevolution equationsspectral analysisunbounded operator coefficientsabstract Gurtin-Pipkin integro-differential equationtheory of heat transfer and acoustics

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Hydro- and aero-acoustics (76Q05) Asymptotics of solutions to integral equations (45M05) Laplace transform (44A10) Abstract integral equations, integral equations in abstract spaces (45N05) Integro-differential operators (47G20)

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Cites Work

• Unnamed Item
• \(L^ 2\)-regularity for parabolic partial integrodifferential equations with delay in the highest-order derivatives
• Heat equation with memory: Lack of controllability to rest
• Non-homogeneous media and vibration theory
• Theory and applications of partial functional differential equations
• The controllability of the Gurtin-Pipkin equation: a cosine operator approach
• A general theory of heat conduction with finite wave speeds

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