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CMFD, 2016, Volume 60, Pages 102–113 (Mi cmfd297)  

This article is cited in 4 scientific papers (total in 4 papers)

On the Dirichlet problem for differential-difference elliptic equations in a half-plane

A. B. Muravnikab

a RUDN University, 6 Miklukho-Maklaya st., Moscow, 117198 Russia
b JSC Concern "Sozvezdie", Voronezh, Russia

Abstract: The Dirichlet problem is considered in a half-plane (with continuous and bounded boundaryvalue function) for the model elliptic differential-difference equation
$$ u_{xx}+au_{xx}(x+h,y)+u_{yy}=0,\qquad|a|<1. $$
Its solvability is proved in the sense of generalized functions, the integral representation of the solution is constructed, and it is proved that everywhere but the boundary hyperplane this solution satisfies the equation in the classic sense as well.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-4479.2014.1
Russian Foundation for Basic Research 14-01-00265


Full text: PDF file (177 kB)
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UDC: 517.929

Citation: A. B. Muravnik, “On the Dirichlet problem for differential-difference elliptic equations in a half-plane”, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 3, CMFD, 60, PFUR, M., 2016, 102–113

Citation in format AMSBIB
\Bibitem{Mur16}
\by A.~B.~Muravnik
\paper On the Dirichlet problem for differential-difference elliptic equations in a~half-plane
\inbook Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22--29, 2014). Part~3
\serial CMFD
\yr 2016
\vol 60
\pages 102--113
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd297}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. B. Muravnik, “Asymptotic Properties of Solutions of the Dirichlet Problem in the Half-Plane for Differential-Difference Elliptic Equations”, Math. Notes, 100:4 (2016), 579–588  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. B. Muravnik, “Asimptoticheskie svoistva reshenii dvumernykh differentsialno-raznostnykh ellipticheskikh zadach”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 63, no. 4, Rossiiskii universitet druzhby narodov, M., 2017, 678–688  mathnet  crossref
    3. A. Muravnik, “On the half-plane Dirichlet problem for differential-difference elliptic equations with several nonlocal terms”, Math. Model. Nat. Phenom., 12:6, SI (2017), 130–143  crossref  mathscinet  zmath  isi  scopus
    4. A. B. Muravnik, “Ellipticheskie zadachi s nelokalnym potentsialom, voznikayuschie v modelyakh nelineinoi optiki”, Matem. zametki, 105:5 (2019), 747–762  mathnet  crossref  elib
  • Современная математика. Фундаментальные направления
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