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Sbornik: Mathematics, 2003, Volume 194, Issue 9, Pages 1411–1426
DOI: https://doi.org/10.1070/SM2003v194n09ABEH000770
(Mi sm770)
 

This article is cited in 20 scientific papers (total in 20 papers)

Spaces of initial data for differential equations in a Hilbert space

R. V. Shamin

Moscow Aviation Institute
References:
Abstract: Spaces of initial data for differential equations in a Hilbert space are considered. Necessary and sufficient conditions for the strong solubility of parabolic differential-difference equations and parabolic functional differential equations with dilated and contracted variables are obtained.
Received: 10.02.2003
Bibliographic databases:
UDC: 517.95
MSC: 35R10, 35K90
Language: English
Original paper language: Russian
Citation: R. V. Shamin, “Spaces of initial data for differential equations in a Hilbert space”, Sb. Math., 194:9 (2003), 1411–1426
Citation in format AMSBIB
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\by R.~V.~Shamin
\paper Spaces of initial data for differential equations in a~Hilbert space
\jour Sb. Math.
\yr 2003
\vol 194
\issue 9
\pages 1411--1426
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Linking options:
  • https://www.mathnet.ru/eng/sm770
  • https://doi.org/10.1070/SM2003v194n09ABEH000770
  • https://www.mathnet.ru/eng/sm/v194/i9/p141
  • This publication is cited in the following 20 articles:
    1. A. L. Tasevich, “Smoothness of Generalized Solutions to the Dirichlet Problem for Strongly Elliptic Functional Differential Equations with Orthotropic Contractions on the Boundary of Adjacent Subdomains”, J Math Sci, 2024  crossref
    2. A. L. Tasevich, “Gladkost obobschennykh reshenii zadachi Dirikhle dlya silno ellipticheskikh funktsionalno-differentsialnykh uravnenii s ortotropnymi szhatiyami na granitse sosednikh podoblastei”, SMFN, 69, no. 1, Rossiiskii universitet druzhby narodov, M., 2023, 152–165  mathnet  crossref
    3. Shaldanbayev A.Sh., Imanbayeva A.B., Beisebayeva A.Zh., Shaldanbayeva A.A., “On the Square Root of the Operator of Sturm-Liouville Fourth-Order”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 3:325 (2019), 85–96  crossref  isi
    4. Shaldanbayev A.Sh., Shaldanbayeva A.A., Shaldanbay B.A., “On Square Root of Sturm-Liuville Operator”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 3:325 (2019), 97–113  crossref  isi
    5. A. L. Skubachevskii, “Boundary-value problems for elliptic functional-differential equations and their applications”, Russian Math. Surveys, 71:5 (2016), 801–906  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. A. L. Tasevich, “Smoothness of generalized solutions of the Dirichlet problem for strongly elliptic functional differential equations with orthotropic contractions”, Journal of Mathematical Sciences, 233:4 (2018), 541–554  mathnet  crossref
    7. L. E. Rossovskii, “Elliptic functional differential equations with contractions and extensions of independent variables of the unknown function”, Journal of Mathematical Sciences, 223:4 (2017), 351–493  mathnet  crossref
    8. M. S. Agranovich, A. M. Selitskii, “Fractional Powers of Operators Corresponding to Coercive Problems in Lipschitz Domains”, Funct. Anal. Appl., 47:2 (2013), 83–95  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. A. M. Selitskii, “Space of Initial Data for the Second Boundary-Value Problem for a Parabolic Differential-Difference Equation in Lipschitz Domains”, Math. Notes, 94:3 (2013), 444–447  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. A. M. Selitskii, “The Space of Initial Data of the 3d Boundary-Value Problem for a Parabolic Differential-Difference Equation in the One-Dimensional Case”, Math. Notes, 92:4 (2012), 580–584  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. L. E. Rossovskii, “On a class of sectorial functional-differential operators”, Diff Equat, 48:2 (2012), 234  crossref  mathscinet  zmath  isi  elib  elib  scopus
    12. L. E. Rossovskii, “The coercivity of functional differential equations”, Journal of Mathematical Sciences, 201:5 (2014), 663–672  mathnet  crossref  mathscinet
    13. L. E. Rossovskii, “Spectral properties of functional-differential operators and a Gårding-type inequality”, Dokl Math, 82:2 (2010), 765  crossref  mathscinet  zmath  isi  elib  scopus
    14. R. V. Shamin, “Approximation of Evolution Differential Equations in Scales of Hilbert Spaces”, Math. Notes, 85:2 (2009), 293–295  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. R. V. Shamin, “Dynamics of ideal liquid with free surface in conformal variables”, Journal of Mathematical Sciences, 160:5 (2009), 537–678  mathnet  crossref  mathscinet  zmath  elib
    16. L. V. Borodulina, L. E. Rossovskii, “Solvability of elliptic functional-differential equations with compressions of the arguments in weighted spaces”, J. Math. Sci. (N. Y.), 143:4 (2007), 3205–3216  mathnet  crossref  mathscinet  elib
    17. A. M. Selitskii, “The third boundary-value problem for parabolic differential-difference equations”, Journal of Mathematical Sciences, 153:5 (2008), 591–611  mathnet  crossref  mathscinet  zmath  elib
    18. A. M. Selitskii, A. L. Skubachevskii, “Second boundary-value problem for parabolic differential-difference equations”, Russian Math. Surveys, 62:1 (2007), 191–192  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. A. M. Selitskii, A. L. Skubachevskii, “The second boundary-value problem for parabolic differential-difference equations”, J. Math. Sci. (N. Y.), 143:4 (2007), 3386–3400  mathnet  crossref  mathscinet  elib
    20. Rossovskii L.E., “Elliptic functionally-differential equations with contractions of arguments”, Dokl. Math., 74:3 (2006), 809–811  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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