Functional difference equations in the problem on the forced oscillations of a fluid in an infinite pool with conical bottom

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Functional difference equations in the problem on the forced oscillations of a fluid in an infinite pool with conical bottom. / Лялинов, Михаил Анатольевич.

In: St. Petersburg Mathematical Journal, Vol. 29, 2018, p. 267-287 .

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{b9006d4cfc11497bb61127f33da3fa7c,

title = "Functional difference equations in the problem on the forced oscillations of a fluid in an infinite pool with conical bottom",

abstract = "The model problem under study concerns the stationary forced oscillations of a fluid of small amplitude under the action of the field of gravity in an infinite pool with sources located on its conical bottom with infiltration. A classical solution of that problem is studied in the linear approximation. By the use of the Mellin transform and expansion in spherical functions, the problem is reduced to a set of systems of functional difference equations with meromorphic coefficients that are combinations of associated Legendre functions and their derivatives. Then, the problem on systems of difference equations reduces to singular integral equations. For this, in particular, solutions of some auxiliary first order functional equations with meromorphic coefficients are computed. It is shown that the system of integral equations in question is Fredholm with index zero. Within some assumptions, the classical solution of the problem exists and is unique. Some estimates of the classical solution in the vicinity of the conic point and at infinity are obtained.",

keywords = "Conic domain, Forced oscillations of a liquid, Fredholm integral equations, Functional equations, functional equations, conic domain",

author = "Лялинов, {Михаил Анатольевич}",

note = "Funding Information: 2010 Mathematics Subject Classification. 35Q35. Key words and phrases. Forced oscillations of a liquid, functional equations, Fredholm integral equations, conic domain. Supported in part by RFBR (grant no. 17-01-00668a).",

year = "2018",

doi = "10.1090/spmj/1493",

language = "English",

volume = "29",

pages = "267--287 ",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

}

RIS

TY - JOUR

T1 - Functional difference equations in the problem on the forced oscillations of a fluid in an infinite pool with conical bottom

AU - Лялинов, Михаил Анатольевич

N1 - Funding Information: 2010 Mathematics Subject Classification. 35Q35. Key words and phrases. Forced oscillations of a liquid, functional equations, Fredholm integral equations, conic domain. Supported in part by RFBR (grant no. 17-01-00668a).

PY - 2018

Y1 - 2018

N2 - The model problem under study concerns the stationary forced oscillations of a fluid of small amplitude under the action of the field of gravity in an infinite pool with sources located on its conical bottom with infiltration. A classical solution of that problem is studied in the linear approximation. By the use of the Mellin transform and expansion in spherical functions, the problem is reduced to a set of systems of functional difference equations with meromorphic coefficients that are combinations of associated Legendre functions and their derivatives. Then, the problem on systems of difference equations reduces to singular integral equations. For this, in particular, solutions of some auxiliary first order functional equations with meromorphic coefficients are computed. It is shown that the system of integral equations in question is Fredholm with index zero. Within some assumptions, the classical solution of the problem exists and is unique. Some estimates of the classical solution in the vicinity of the conic point and at infinity are obtained.

AB - The model problem under study concerns the stationary forced oscillations of a fluid of small amplitude under the action of the field of gravity in an infinite pool with sources located on its conical bottom with infiltration. A classical solution of that problem is studied in the linear approximation. By the use of the Mellin transform and expansion in spherical functions, the problem is reduced to a set of systems of functional difference equations with meromorphic coefficients that are combinations of associated Legendre functions and their derivatives. Then, the problem on systems of difference equations reduces to singular integral equations. For this, in particular, solutions of some auxiliary first order functional equations with meromorphic coefficients are computed. It is shown that the system of integral equations in question is Fredholm with index zero. Within some assumptions, the classical solution of the problem exists and is unique. Some estimates of the classical solution in the vicinity of the conic point and at infinity are obtained.

KW - Conic domain

KW - Forced oscillations of a liquid

KW - Fredholm integral equations

KW - Functional equations

KW - functional equations

KW - conic domain

UR - http://www.ams.org/journals/spmj/2018-29-02/S1061-0022-2018-01493-X/

UR - http://www.scopus.com/inward/record.url?scp=85043513015&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/functional-difference-equations-problem-forced-oscillations-fluid-infinite-pool-conical-bottom

U2 - 10.1090/spmj/1493

DO - 10.1090/spmj/1493

M3 - Article

VL - 29

SP - 267

EP - 287

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

ER -

ID: 23781558