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.
\Bibitem{Sha03}
\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
\mathnet{http://mi.mathnet.ru/eng/sm770}
\crossref{https://doi.org/10.1070/SM2003v194n09ABEH000770}
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This publication is cited in the following 20 articles:
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
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
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
A. L. Skubachevskii, “Boundary-value problems for elliptic functional-differential equations and their applications”, Russian Math. Surveys, 71:5 (2016), 801–906
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
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
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
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
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
L. E. Rossovskii, “On a class of sectorial functional-differential operators”, Diff Equat, 48:2 (2012), 234
L. E. Rossovskii, “The coercivity of functional differential equations”, Journal of Mathematical Sciences, 201:5 (2014), 663–672
L. E. Rossovskii, “Spectral properties of functional-differential operators and a Gårding-type inequality”, Dokl Math, 82:2 (2010), 765
R. V. Shamin, “Approximation of Evolution Differential Equations in Scales of Hilbert Spaces”, Math. Notes, 85:2 (2009), 293–295
R. V. Shamin, “Dynamics of ideal liquid with free surface in conformal variables”, Journal of Mathematical Sciences, 160:5 (2009), 537–678
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
A. M. Selitskii, “The third boundary-value problem for parabolic differential-difference equations”, Journal of Mathematical Sciences, 153:5 (2008), 591–611
A. M. Selitskii, A. L. Skubachevskii, “Second boundary-value problem for parabolic differential-difference equations”, Russian Math. Surveys, 62:1 (2007), 191–192
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
Rossovskii L.E., “Elliptic functionally-differential equations with contractions of arguments”, Dokl. Math., 74:3 (2006), 809–811