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Uspekhi Mat. Nauk, 1960, Volume 15, Issue 2(92), Pages 97–154 (Mi umn6720)  

This article is cited in 50 scientific papers (total in 50 papers)

The solvability of mixed problems for hyperbolic and parabolic equations

V. A. Il'in


Full text: PDF file (6023 kB)

English version:
Russian Mathematical Surveys, 1960, 15:1, 85–142

Bibliographic databases:

MSC: 35M10, 35L05, 35Kxx, 42Axx
Received: 08.04.1959

Citation: V. A. Il'in, “The solvability of mixed problems for hyperbolic and parabolic equations”, Uspekhi Mat. Nauk, 15:2(92) (1960), 97–154; Russian Math. Surveys, 15:1 (1960), 85–142

Citation in format AMSBIB
\Bibitem{Ili60}
\by V.~A.~Il'in
\paper The solvability of mixed problems for hyperbolic and parabolic equations
\jour Uspekhi Mat. Nauk
\yr 1960
\vol 15
\issue 2(92)
\pages 97--154
\mathnet{http://mi.mathnet.ru/umn6720}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=118952}
\zmath{https://zbmath.org/?q=an:0116.29802}
\transl
\jour Russian Math. Surveys
\yr 1960
\vol 15
\issue 1
\pages 85--142
\crossref{https://doi.org/10.1070/RM1960v015n02ABEH004217}


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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. V. R. Nosov, “On a mixed problem for a hyperbolic equation of the second order”, Math. USSR-Izv., 3:2 (1969), 357–374  mathnet  crossref  mathscinet  zmath
    2. Yu. B. Orochko, “On the application of spectral theory to obtain estimates of solutions of the Schrödinger equation”, Math. USSR-Sb., 22:2 (1974), 167–186  mathnet  crossref  mathscinet  zmath
    3. Hsiao G.C., Weinacht R.J., “Singular perturbations for a semilinear hyperbolic equation”, SIAM J. Math. Anal., 14:6 (1983), 1168–1179  crossref  mathscinet  zmath  isi
    4. S. I. Lyashko, “On the solubility of mixed boundary-value problems with operator-valued coefficients”, Russian Math. Surveys, 42:3 (1987), 224–225  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. V. N. Denisov, “On the behaviour of solutions of parabolic equations for large values of time”, Russian Math. Surveys, 60:4 (2005), 721–790  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. V. A. Il'in, E. I. Moiseev, “Optimization of boundary controls of string vibrations”, Russian Math. Surveys, 60:6 (2005), 1093–1119  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. V. A. Il'in, “Optimization of the Boundary Control of an Elastic Force at One Endpoint of a String with the Other Endpoint Fixed”, Proc. Steklov Inst. Math., 248 (2005), 111–117  mathnet  mathscinet  zmath
    8. Il'in, VA, “Optimization of a boundary control by a displacement at one end of a string based on minimization of the integral of the modulus of the derivative of the displacement raised to an arbitrary power p >= 1”, Doklady Mathematics, 74:3 (2006), 878  crossref  isi  elib
    9. Denisov, VN, “Necessary and sufficient conditions for the stabilization of the solution to the Dirichlet problem for the heat equation”, Doklady Mathematics, 73:2 (2006), 193  mathnet  crossref  mathscinet  isi  elib
    10. Il'in, VA, “Optimization of the boundary control of string vibrations by an elastic force on an arbitrary sufficiently large time interval”, Differential Equations, 42:12 (2006), 1775  mathnet  crossref  mathscinet  isi  elib
    11. Il'in, VA, “Minimization of the L (p)-norm with arbitrary p >= 1 of the derivative of a boundary displacement control on an arbitrary sufficiently large time interval T”, Differential Equations, 42:11 (2006), 1633  mathnet  crossref  mathscinet  isi
    12. Il'in V.A., Moiseev E.I., “Optimization of a boundary control of an elastic force at one end of a string based on minimization of the integral of the modulus of the elastic force raised to an arbitrary power $p\ge 1$”, Dokl. Math., 75:1 (2007), 123–126  mathnet  crossref  mathscinet  isi  elib  elib
    13. Il'in, VA, “Optimal boundary control by the displacement of one endpoint of the string with the other endpoint being free in an arbitrarily large time interval”, Differential Equations, 43:10 (2007), 1403  crossref  isi
    14. Il'in, AVA, “Optimization of a boundary control by a displacement at one end of a string with second end free during an arbitrary sufficiently large time interval”, Doklady Mathematics, 76:3 (2007), 806  crossref  isi  elib
    15. Il'in, VA, “Optimization of boundary controls by displacements at two ends of a string during an arbitrary sufficiently large time interval”, Doklady Mathematics, 76:3 (2007), 828  crossref  isi  elib
    16. Moiseev, EI, “Optimal boundary control by a displacement in W'(p) of a string with free end”, Differential Equations, 44:5 (2008), 730  crossref  mathscinet  zmath  isi  elib
    17. Il'in, VA, “Optimization of the control by elastic boundary forces at two ends of a string in an arbitrarily large time interval”, Differential Equations, 44:1 (2008), 92  mathscinet  isi  elib
    18. V. A. Il'in, E. I. Moiseev, “Optimization of the boundary control by shift or elastic force at one end of string in a sufficiently long arbitrary time”, Autom. Remote Control, 69:3 (2008), 354–362  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    19. L. I. Bloshanskaya, I. N. Smirnov, “Optimal boundary control by an elastic force at one end and a displacement at the other end for an arbitrary sufficiently large time interval in the string vibration problem”, Differ. Equ., 45:6 (2009), 878–888  crossref  mathscinet  zmath  isi  elib  elib
    20. Sazonov A.Yu., Fomicheva Yu.G., “O suschestvovanii i edinstvennosti klassicheskogo resheniya smeshannoi zadachi dlya giperbolicheskogo uravneniya vtorogo poryadka, soderzhaschego operator Besselya po chasti prostranstvennykh peremennykh”, Vestn. Tambovskogo un-ta. Ser.: Estestvennye i tekhnicheskie nauki, 14:1 (2009), 321–324  mathscinet  elib
    21. Nesterenko Yu.R., “Mixed problem for the wave equation with Robin boundary conditions”, Dokl. Math., 79:3 (2009), 322–324  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    22. Moiseev E.I., Kholomeeva A.A., “Optimization of the boundary control of string vibrations in the excitation problem with a fixed endpoint in the class $W_2^2$”, Differ. Equ., 45:5 (2009), 757–761  crossref  mathscinet  zmath  isi  elib  elib
    23. Katrakhova A.A., Sazonov A.Yu., Fomicheva Yu.G., “O suschestvovanii i edinstvennosti klassicheskogo resheniya smeshannoi zadachi dlya singulyarnogo giperbolicheskogo uravneniya, soderzhaschego operator Besselya”, Vestn. Tambovskogo un-ta. Ser.: Estestvennye i tekhnicheskie nauki, 14:6-2 (2009), 1342–1360  elib
    24. V. A. Il'in, “A terminal–boundary value problem that describes the process of damping the vibrations of a rod consisting of two segments with different densities and elasticity coefficients but with identical wave travel times”, Proc. Steklov Inst. Math., 269 (2010), 127–136  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    25. Hasanov K.K., Gasumov T.M., “Minimal Energy Control for the Wave Equation With Non-Classical Boundary Condition”, Applied and Computational Mathematics, 9:1 (2010), 47–56  isi
    26. Lomov I.S., “Negladkie sobstvennye funktsii v zadachakh matematicheskoi fiziki”, Differentsialnye uravneniya, 47:3 (2011), 358–365  elib
    27. Smirnov I.N., “Reshenie smeshannykh zadach s granichnym upravleniem uprugoi siloi dlya telegrafnogo uravneniya”, Differentsialnye uravneniya, 47:3 (2011), 433–441  elib
    28. Petrova E.V., Provotorov V.V., “Obobschennaya zadacha neimana na grafe-zvezde”, Matematika i ee prilozheniya. zhurnal ivanovskogo matematicheskogo obschestva, 2011, no. 1, 85–94  elib
    29. Aliev A.B., Shukyurova G.D., “Zadacha koshi dlya giperbolicheskogo operatorno-differentsialnogo uravneniya vtorogo poryadka s singulyarnym koeffitsientom”, Differentsialnye uravneniya, 47:6 (2011), 880–884  elib
    30. V. A. Il'in, “On the complete damping of oscillations of an inhomogeneous rod by means of a boundary control at one end”, Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S97–S105  mathnet  crossref  isi  elib
    31. Ilin V.A., Kuleshov A.A., “Ob opredelenii obobschennogo iz klassa l_{p} resheniya smeshannoi zadachi dlya volnovogo uravneniya cherez integralnoe tozhdestvo”, Doklady akademii nauk, 447:3 (2012), 247–247  elib
    32. Ilin V.A., Kuleshov A.A., “Obobschennye resheniya volnovogo uravneniya iz klassov $L_{p}$ i $W_p^1$ pri $P$ 1”, Doklady akademii nauk, 446:4 (2012), 374–374  elib
    33. Ilin V.A., Kuleshov A.A., “O nekotorykh svoistvakh obobschennykh reshenii volnovogo uravneniya iz klassov $L_p$ i $W_p^1$ pri $p\geq 1$”, Differentsialnye uravneniya, 48:11 (2012), 1493–1493  elib
    34. V. A. Il'in, A. A. Kuleshov, “Equivalence of two definitions of a generalized $L_p$ solution to the initial-boundary value problem for the wave equation”, Proc. Steklov Inst. Math., 284 (2014), 155–160  mathnet  crossref  crossref  isi  elib  elib
    35. A. P. Khromov, M. Sh. Burlutskaya, “Klassicheskoe reshenie metodom Fure smeshannykh zadach pri minimalnykh trebovaniyakh na iskhodnye dannye”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:2 (2014), 171–198  mathnet
    36. Nikolay Kuznetsov, Avgust Khromov, “The Fourier Method in Russia Before and After V. A. Steklov”, Math Intelligencer, 36:4 (2014), 67  crossref
    37. A. P. Khromov, “O klassicheskom reshenii odnoi smeshannoi zadachi dlya volnovogo uravneniya”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 15:1 (2015), 56–66  mathnet  crossref  elib
    38. A. A. Gimaltdinova, K. V. Kurman, “O polnote odnoi pary biortogonalno sopryazhennykh sistem funktsii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 7–18  mathnet  crossref  zmath  elib
    39. M. Sh. Burlutskaya, A. P. Khromov, “The resolvent approach for the wave equation”, Comput. Math. Math. Phys., 55:2 (2015), 227–239  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    40. V. V. Kornev, A. P. Khromov, “A resolvent approach in the Fourier method for the wave equation: The non-selfadjoint case”, Comput. Math. Math. Phys., 55:7 (2015), 1138–1149  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    41. V. V. Kornev, A. P. Khromov, “Resolvent approach to the Fourier method in a mixed problem for the wave equation”, Comput. Math. Math. Phys., 55:4 (2015), 618–627  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    42. A. A. Dryazhenkov, M. M. Potapov, “Numerical solution of the positional boundary control problem for the wave equation with unknown initial data”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 22–30  mathnet  crossref  crossref  mathscinet  isi  elib
    43. V. K. Andreev, “O reshenii odnoi obratnoi zadachi, modeliruyuschei dvumernoe dvizhenie vyazkoi zhidkosti”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:4 (2016), 5–16  mathnet  crossref  elib
    44. Lomovtsev F.E. Novikov E.N., “Factorized equation of vibrations of a finite string with nonstationary second directional derivatives at the endpoints”, Differ. Equ., 52:6 (2016), 781–788  crossref  isi
    45. T. K. Yuldashev, “Ob odnoi nelokalnoi zadache dlya neodnorodnogo integro-differentsialnogo uravneniya tipa Bussineska s vyrozhdennym yadrom”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 159, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2017, 88–99  mathnet  mathscinet  elib
    46. T. K. Yuldashev, “Obobschennaya razreshimost smeshannoi zadachi dlya nelineinogo integro-differentsialnogo uravneniya vysokogo poryadka s vyrozhdennym yadrom”, Izv. IMI UdGU, 50 (2017), 121–132  mathnet  crossref  elib
    47. V. P. Kurdyumov, A. P. Khromov, V. A. Khalova, “Smeshannaya zadacha dlya volnovogo uravneniya s nenulevoi nachalnoi skorostyu”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:2 (2018), 157–171  mathnet  crossref  elib
    48. P. V. Babich, V. B. Levenshtam, “Recovery of a Rapidly Oscillating Absolute Term in the Multidimensional Hyperbolic Equation”, Math. Notes, 104:4 (2018), 489–497  mathnet  crossref  crossref  isi  elib
    49. I. S. Mokrousov, “Kriterii prinadlezhnosti klassu $W^l_p$ obobschennogo iz klassa $L_p$ resheniya volnovogo uravneniya”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:3 (2018), 297–304  mathnet  crossref  elib
    50. Dryazhenkov A.A., Potapov M.M., “Numerical Method For Damping String Vibrations With Unknown Initial State in the Class of Weak Generalized Solutions”, Differ. Equ., 54:11 (2018), 1425–1443  crossref  zmath  isi  scopus
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