N. A. Rautian, “On the Structure and Properties of Solutions of Integro-Differential Equations Arising in Thermal Physics and Acoustics”, Mat. Zametki, 90:3 (2011), 470–473; Math. Notes, 90:3 (2011), 455

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Matematicheskie Zametki, 2011, Volume 90, Issue 3, Pages 470–473
DOI: https://doi.org/10.4213/mzm9226 (Mi mzm9226)

This article is cited in 13 scientific papers (total in 13 papers)

Brief Communications

On the Structure and Properties of Solutions of Integro-Differential Equations Arising in Thermal Physics and Acoustics

N. A. Rautian

Plekhanov Russian State University of Economics, Moscow

Full-text PDF (312 kB) Citations (13)

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DOI: https://doi.org/10.4213/mzm9226

Keywords: integro-differential equation, unbounded operator coefficient, exponential series, Hilbert space, the Sobolev space $W_1^1(\mathbb R_+)$, self-adjoint operator, Laplace transform.

Received: 16.03.2011

English version:
Mathematical Notes, 2011, Volume 90, Issue 3, Pages 455–459
DOI: https://doi.org/10.1134/S000143461109015X

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: N. A. Rautian, “On the Structure and Properties of Solutions of Integro-Differential Equations Arising in Thermal Physics and Acoustics”, Mat. Zametki, 90:3 (2011), 470–473; Math. Notes, 90:3 (2011), 455–459

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm9226

https://doi.org/10.4213/mzm9226

https://www.mathnet.ru/eng/mzm/v90/i3/p470

This publication is cited in the following 13 articles:

V. V. Vlasov, N. A. Rautian, “Investigation of Integro-Differential Equations by Methods of Spectral Theory”, J Math Sci, 278:1 (2024), 55
Igor Romanov, Alexey Shamaev, Lecture Notes in Civil Engineering, 282, Proceedings of FORM 2022, 2023, 223
I. V. Romanov, A. S. Shamaev, “Exact Control of a Distributed System Described by the Wave Equation with Integral Memory”, J Math Sci, 262:3 (2022), 358
A V Romanova, I V Romanov, “On the problems of controllability and uncontrollability for some mechanical systems described by the equations of vibrations of plates and beams with integral memory”, IOP Conf. Ser.: Mater. Sci. Eng., 1083:1 (2021), 012041
A. V. Davydov, Yu. A. Tikhonov, “On Properties of the Spectrum of an Operator Pencil Arising in Viscoelasticity Theory”, Math. Notes, 103:5 (2018), 841–845
Ortiz R.P., Rautian N.A., “Representation of solutions of integro-differential equations with kernels depending on the parameter”, Differ. Equ., 53:1 (2017), 139–143
Romanov I., Shamaev A., “Noncontrollability to Rest of the Two-Dimensional Distributed System Governed by the Integrodifferential Equation”, J. Optim. Theory Appl., 170:3 (2016), 772–782
I. V. Romanov, A. S. Shamaev, “Some problems of distributed and boundary control for systems with integral aftereffect”, J. Math. Sci. (N. Y.), 234:4 (2018), 470–484
V. V. Vlasov, R. Perez Ortiz, “Spectral Analysis of Integro-Differential Equations in Viscoelasticity and Thermal Physics”, Math. Notes, 98:4 (2015), 689–693
V. V. Vlasov, N. A. Rautian, “Spectral analysis and representations of solutions to abstract integrodifferential equations”, Dokl. Math., 89:1 (2014), 34–37
V. V. Vlasov, N. A. Rautian, “Properties of solutions of integro-differential equations arising in heat and mass transfer theory”, Trans. Moscow Math. Soc., 75 (2014), 185–204
I. V. Romanov, A. S. Shamaev, “On the problem of precise control of the system obeying the delay string equation”, Autom. Remote Control, 74:11 (2013), 1810–1819
I. Romanov, A. Shamaev, “Exact controllability of the distributed system, governed by string equation with memory”, J. Dyn. Control Syst., 19:4 (2013), 611–623

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	616
Full-text PDF :	253
References:	79
First page:	21

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