Yu. E. Anikonov, M. V. Neshchadim, “Representations for the solutions and coefficients of evolution equations”, Sib. Zh. Ind. Mat., 16:2 (2013), 40–49; J. Appl. Industr. Math., 7:3 (2013), 326

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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 2, Pages 40–49 (Mi sjim778)

This article is cited in 12 scientific papers (total in 12 papers)

Representations for the solutions and coefficients of evolution equations

Yu. E. Anikonov^ab, M. V. Neshchadim^ba

^a Sobolev Institute of Mathematics of SB RAS, 4 Koptyug av., 630090 Novosibirsk, Russia
^b Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk, Russia

Full-text PDF (235 kB) Citations (12)

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Abstract: We give new representations for the solutions and coefficients of evolution equations in the linear case. The obtained formulas contain functional arbitrariness, which can be used in identification problems. We also give classes of hyperbolic equations admitting generalized functional-invariant solutions.

Keywords: second-order evolution differential equations, Poisson formula, generalized functional-invariant solutions.

Received: 22.03.2013

English version:
Journal of Applied and Industrial Mathematics, 2013, Volume 7, Issue 3, Pages 326–334
DOI: https://doi.org/10.1134/S1990478913030058

Bibliographic databases:

Document Type: Article

UDC: 517.9

Language: Russian

Citation: Yu. E. Anikonov, M. V. Neshchadim, “Representations for the solutions and coefficients of evolution equations”, Sib. Zh. Ind. Mat., 16:2 (2013), 40–49; J. Appl. Industr. Math., 7:3 (2013), 326–334

Citation in format AMSBIB

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\by Yu.~E.~Anikonov, M.~V.~Neshchadim

\paper Representations for the solutions and coefficients of evolution equations

\jour Sib. Zh. Ind. Mat.

\yr 2013

\vol 16

\issue 2

\pages 40--49

\mathnet{http://mi.mathnet.ru/sjim778}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3203340}

\transl

\jour J. Appl. Industr. Math.

\yr 2013

\vol 7

\issue 3

\pages 326--334

\crossref{https://doi.org/10.1134/S1990478913030058}

Linking options:

https://www.mathnet.ru/eng/sjim778

https://www.mathnet.ru/eng/sjim/v16/i2/p40

This publication is cited in the following 12 articles:

M. V. Neschchadim, A. A. Simonov, “Backlund transformations of the relativistic Schrodinger equation”, J. Appl. Industr. Math., 17:4 (2023), 828–841
Yu. E. Anikonov, “A uniqueness theorem for an inverse kinematic seismic problem”, J. Appl. Industr. Math., 14:1 (2020), 1–5
Anikonov Yu.E. Ayupova N.B. Neshchadim V M., “Some Representations of Solutions to Blokhintsev Equation”, Sib. Electron. Math. Rep., 17 (2020), 1697–1709
Anikonov Yu.E., “Formulas in the Theory of Identification”, Sib. Electron. Math. Rep., 17 (2020), 1522–1539
M. V. Neshchadim, “Functional-invariant solutions to the Maxwell system”, J. Appl. Industr. Math., 11:1 (2017), 107–114
M. V. Neshchadim, “Generalized functional invariant solutions of wave equation for dimension 2”, J. Math. Sci., 237:4 (2019), 569–575
Yu. E. Anikonov, M. V. Neshchadim, “The method of differential relations and nonlinear inverse problems”, J. Appl. Industr. Math., 9:3 (2015), 317–327
Yu. E. Anikonov, M. V. Neshchadim, “Differential identities for nonlinear equations with partial derivatives”, J. Math. Sci., 215:4 (2016), 436–443
Yu. E. Anikonov, M. V. Neshchadim, “Algebra-analytical ways of constructing solutions of differential equations and inverse problems”, J. Math. Sci., 215:4 (2016), 444–459
Yu. E. Anikonov, “Differentsialnye tozhdestva dlya uravnenii s chastnymi proizvodnymi”, Sib. zhurn. industr. matem., 17:2 (2014), 11–17
M. V. Neshchadim, “Sphere Generalized Functional Invariant Solutions of Wave Equation”, J. Math. Sci., 211:6 (2015), 805–810
Yu. E. Anikonov, N. B. Ayupova, “The Hopf–Cole transformation and multidimensional representations of solutions to evolution equations”, J. Appl. Industr. Math., 9:1 (2015), 11–17

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

Сибирский журнал индустриальной математики

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