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Mat. Sb., 2003, Volume 194, Number 9, Pages 141–156 (Mi msb770)  

This article is cited in 16 scientific papers (total in 16 papers)

Spaces of initial data for differential equations in a Hilbert space

R. V. Shamin

Moscow Aviation Institute

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.

DOI: https://doi.org/10.4213/sm770

Full text: PDF file (308 kB)
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English version:
Sbornik: Mathematics, 2003, 194:9, 1411–1426

Bibliographic databases:

UDC: 517.95
MSC: 35R10, 35K90
Received: 10.02.2003

Citation: R. V. Shamin, “Spaces of initial data for differential equations in a Hilbert space”, Mat. Sb., 194:9 (2003), 141–156; Sb. Math., 194:9 (2003), 1411–1426

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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
    7. 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
    8. 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
    9. A. M. Selitskii, “The Space of Initial Data of the $3$d 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
    10. L. E. Rossovskii, “On a class of sectorial functional-differential operators”, Diff Equat, 48:2 (2012), 234  crossref  mathscinet  zmath  isi  elib  elib  scopus
    11. L. E. Rossovskii, “The coercivity of functional differential equations”, Journal of Mathematical Sciences, 201:5 (2014), 663–672  mathnet  crossref  mathscinet
    12. 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
    13. 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
    14. 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
    15. 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
    16. 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
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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