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CMFD, 2014, Volume 52, Pages 3–141 (Mi cmfd264)  

This article is cited in 11 scientific papers (total in 11 papers)

Functional differential parabolic equations: integral transformations and qualitative properties of solutions of the Cauchy problem

A. B. Muravnik

JSC "Concern "Sozvezdie", Voronezh, Russia

Abstract: In this monograph, we examine the Cauchy problem for second-order parabolic functional differential equations containing, in addition to differential operators, translation (generalized translation) operators acting with respect to spatial variables. The specified problems have important applications, such as the multilayer plates and envelopes theory, the diffusion processes theory, including biomathematical applications, models of nonlinear optics, etc. The main concern of the present work is the long-time behavior of solutions of studied problems.

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English version:
Journal of Mathematical Sciences, 2016, 216:3, 345–496

UDC: 517.9

Citation: A. B. Muravnik, “Functional differential parabolic equations: integral transformations and qualitative properties of solutions of the Cauchy problem”, Partial differential equations, CMFD, 52, PFUR, M., 2014, 3–141; Journal of Mathematical Sciences, 216:3 (2016), 345–496

Citation in format AMSBIB
\by A.~B.~Muravnik
\paper Functional differential parabolic equations: integral transformations and qualitative properties of solutions of the Cauchy problem
\inbook Partial differential equations
\serial CMFD
\yr 2014
\vol 52
\pages 3--141
\publ PFUR
\publaddr M.
\jour Journal of Mathematical Sciences
\yr 2016
\vol 216
\issue 3
\pages 345--496

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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. 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
    3. 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
    4. V. V. Katrakhov, S. M. Sitnik, “Metod operatorov preobrazovaniya i kraevye zadachi dlya singulyarnykh ellipticheskikh uravnenii”, Singulyarnye differentsialnye uravneniya, SMFN, 64, no. 2, Rossiiskii universitet druzhby narodov, M., 2018, 211–426  mathnet  crossref
    5. Sh. T. Karimov, “On one method for the solution of an analog of the Cauchy problem for a polycaloric equation with singular Bessel operator”, Ukr. Math. J., 69:10 (2018), 1593–1606  crossref  mathscinet  zmath  isi  scopus
    6. Sh.T. Karimov, “Analog zadachi Koshi dlya neodnorodnogo mnogomernogo polikaloricheskogo uravneniya s operatorom Besselya”, Matematicheskii analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 156, VINITI RAN, M., 2018, 3–17  mathnet  mathscinet
    7. E. L. Shishkina, “Obschee uravnenie Eilera—Puassona—Darbu i giperbolicheskie $B$-potentsialy”, Uravneniya v chastnykh proizvodnykh, SMFN, 65, no. 2, Rossiiskii universitet druzhby narodov, M., 2019, 157–338  mathnet  crossref
    8. F. G. Khushtova, “Vtoraya kraevaya zadacha v polupolose dlya B-parabolicheskogo uravneniya s proizvodnoi Gerasimova-Kaputo po vremeni”, Vestnik KRAUNTs. Fiz.-mat. nauki, 33:4 (2020), 37–50  mathnet  crossref
    9. F. G. Khushtova, “Third Boundary-Value Problem in the Half-Strip for the $B$-Parabolic Equation”, Math. Notes, 109:2 (2021), 292–301  mathnet  crossref  crossref  mathscinet  isi
    10. N. V. Zaitseva, “Uniqueness of the Solution of a Nonlocal Problem for an Elliptic-Hyperbolic Equation with Singular Coefficients”, Math. Notes, 109:4 (2021), 563–569  mathnet  crossref  crossref  isi
    11. O. V. Solonukha, “O razreshimosti lineinoi parabolicheskoi zadachi s nelokalnymi kraevymi usloviyami”, Posvyaschaetsya pamyati professora N.D. Kopachevskogo, SMFN, 67, no. 2, Rossiiskii universitet druzhby narodov, M., 2021, 349–362  mathnet  crossref
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