RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 1957, Volume 12, Issue 3(75), Pages 3–73 (Mi umn7611)  

This article is cited in 39 scientific papers (total in 39 papers)

Discontinuous solutions of non-linear differential equations

O. A. Oleinik


Full text: PDF file (6366 kB)

Bibliographic databases:


Citation: O. A. Oleinik, “Discontinuous solutions of non-linear differential equations”, Uspekhi Mat. Nauk, 12:3(75) (1957), 3–73

Citation in format AMSBIB
\Bibitem{Ole57}
\by O.~A.~Oleinik
\paper Discontinuous solutions of non-linear differential equations
\jour Uspekhi Mat. Nauk
\yr 1957
\vol 12
\issue 3(75)
\pages 3--73
\mathnet{http://mi.mathnet.ru/umn7611}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=94541}
\zmath{https://zbmath.org/?q=an:0131.31803|0080.07701}


Linking options:
  • http://mi.mathnet.ru/eng/umn7611
  • http://mi.mathnet.ru/eng/umn/v12/i3/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. S. N. Kruzhkov, “First order quasilinear equations in several independent variables”, Math. USSR-Sb., 10:2 (1970), 217–243  mathnet  crossref  mathscinet  zmath
    2. V. A. Trenogin, “The development and applications of the asymptotic method of Lyusternik and Vishik”, Russian Math. Surveys, 25:4 (1970), 119–156  mathnet  crossref  mathscinet  zmath
    3. N. V. Krylov, “Some new results in the theory of controlled diffusion processes”, Math. USSR-Sb., 37:1 (1980), 133–149  mathnet  crossref  mathscinet  zmath  isi
    4. V. P. Maslov, G. A. Omel'yanov, “Asymptotic soliton-form solutions of equations with small dispersion”, Russian Math. Surveys, 36:3 (1981), 73–149  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. V. P. Maslov, “Non-standard characteristics in asymptotic problems”, Russian Math. Surveys, 38:6 (1983), 1–42  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. I. I. Danilyuk, “On the Stefan problem”, Russian Math. Surveys, 40:5 (1985), 157–223  mathnet  crossref  mathscinet  zmath  adsnasa
    7. A. S. Kalashnikov, “Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations”, Russian Math. Surveys, 42:2 (1987), 169–222  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. S. N. Kruzhkov, N. S. Petrosyan, “Asymptotic behaviour of the solutions of the Cauchy problem for non-linear first order equations”, Russian Math. Surveys, 42:5 (1987), 1–47  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. A. M. Il'in, “On the asymptotics of the solution of a problem with a small parameter”, Math. USSR-Izv., 34:2 (1990), 261–279  mathnet  crossref  mathscinet  zmath
    10. B. Dakoronya, “Slabaya nepreryvnost i slabaya polunepreryvnost snizu nelineinykh funktsionalov”, UMN, 44:4(268) (1989), 35–98  mathnet  mathscinet  zmath
    11. Yu. V. Egorov, “A contribution to the theory of generalized functions”, Russian Math. Surveys, 45:5 (1990), 1–49  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. I. Veinan, Yu. G. Rykov, Ya. G. Sinai, “The Lax–Oleinik variational principle for some one-dimensional systems of quasilinear equations”, Russian Math. Surveys, 50:1 (1995), 220–222  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. V. V. Chistyakov, “Weak solutions to Burgers-type equations with nonsmooth data”, Math. Notes, 58:3 (1995), 1005–1009  mathnet  crossref  mathscinet  zmath  isi
    14. W. E, Ya. G. Sinai, “Recent results on mathematical and statistical hydrodynamics”, Russian Math. Surveys, 55:4 (2000), 635–666  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. G. L. Litvinov, V. P. Maslov, G. B. Shpiz, “Idempotent Functional Analysis: An Algebraic Approach”, Math. Notes, 69:5 (2001), 696–729  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. A. Yu. Shcheglov, “A method for approximate solution in $C^2$ of a hyperbolic equation with Lipschitz nonlinearity”, Comput. Math. Math. Phys., 41:3 (2001), 392–406  mathnet  mathscinet  zmath  elib
    17. Rublev, IV, “The relationship between two approaches to a generalized solution of the Hamilton–Jacobi equation”, Differential Equations, 38:6 (2002), 865  mathnet  crossref  isi  elib
    18. A. G. Malyshkin, “Limit Dynamics for Stochastic Models of Data Exchange in Parallel Computation Networks”, Problems Inform. Transmission, 42:3 (2006), 234–250  mathnet  crossref  mathscinet  elib  elib
    19. Sinai, YG, “Mathematical results related to the Navier–Stokes system”, Spde in Hydrodynamic: Recent Progress and Prospects, 1942 (2008), 151  crossref  isi  elib
    20. V. A. Galaktionov, S. I. Pokhozhaev, “Third-order nonlinear dispersive equations: Shocks, rarefaction, and blowup waves”, Comput. Math. Math. Phys., 48:10 (2008), 1784–1810  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    21. A. V. Gasnikov, “Convergence in the form of a solution to the Cauchy problem for a quasilinear parabolic equation with a monotone initial condition to a system of waves”, Comput. Math. Math. Phys., 48:8 (2008), 1376–1405  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    22. A. V. Gasnikov, “Time-asymptotic behaviour of a solution of the Cauchy initial-value problem for a conservation law with non-linear divergent viscosity”, Izv. Math., 73:6 (2009), 1111–1148  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    23. Kozlova A.K., “Svoistva sistemy uravnenii i struktura reshenii zadachi vytesneniya nefti smesyami gazov”, Tr. Rossiiskogo gos. un-ta nefti i gaza im. I. M. Gubkina, 2009, no. 3, 91–102  elib
    24. A. V. Karakin, “The generalized Backley–Leverett problem”, Math. Models Comput. Simul., 3:2 (2011), 135–148  mathnet  crossref  mathscinet
    25. I. M. Prudnikov, “$C^2(D)$-integralnye approksimatsii negladkikh funktsii, sokhranyayuschie $\varepsilon(D)$-tochki lokalnykh ekstremumov”, Tr. IMM UrO RAN, 16, no. 5, 2010, 159–169  mathnet  elib
    26. S. V. Zakharov, “The Cauchy problem for a quasilinear parabolic equation with a large initial gradient and low viscosity”, Comput. Math. Math. Phys., 50:4 (2010), 665–672  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    27. Kozlov V.V., “Ob uravneniyakh dvizheniya besstolknovitelnoi sploshnoi sredy”, Prikladnaya matematika i mekhanika, 75:6 (2011), 883–990  elib
    28. S. Bianchini, “SBV regularity of systems of conservation laws and Hamilton–Jacobi equations”, Journal of Mathematical Sciences, 201:6 (2014), 733–745  mathnet  crossref
    29. E. Yu. Panov, “Renormalized entropy solutions of the Cauchy problem for a first-order inhomogeneous quasilinear equation”, Sb. Math., 204:10 (2013), 1480–1515  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    30. V. A. Korneev, “Construction of generalized solution for first order divergence type equation”, Ufa Math. J., 5:3 (2013), 77–93  mathnet  crossref  elib
    31. A. B. Shabat, “Periodic solutions of the Hopf equation”, Theoret. and Math. Phys., 177:2 (2013), 1471–1478  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    32. M. Kh. Numan Elsheikh, D. O. Ogun, Yu. N. Orlov, R. V. Pleshakov, V. Zh. Sakbaev, “Usrednenie sluchainykh polugrupp i neodnoznachnost kvantovaniya gamiltonovykh sistem”, Preprinty IPM im. M. V. Keldysha, 2014, 019, 28 pp.  mathnet
    33. L. S. Efremova, V. Zh. Sakbaev, “Notion of blowup of the solution set of differential equations and averaging of random semigroups”, Theoret. and Math. Phys., 185:2 (2015), 1582–1598  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    34. G. M. Henkin, A. A. Shananin, “Cauchy–Gelfand Problem and the Inverse Problem for a First-Order Quasilinear Equation”, Funct. Anal. Appl., 50:2 (2016), 131–142  mathnet  crossref  crossref  mathscinet  isi  elib
    35. A. V. Fedorov, I. A. Bedarev, “The shock waves structure in the gas-particles mixture with chaotic pressure”, Math. Models Comput. Simul., 10:1 (2018), 1–14  mathnet  crossref  elib
    36. S. V. Zakharov, “Dvukhparametricheskie asimptotiki v bisingulyarnoi zadache Koshi dlya parabolicheskogo uravneniya”, Tr. IMM UrO RAN, 23, no. 2, 2017, 94–103  mathnet  crossref  elib
    37. A. Zh. Baev, S. V. Bogomolov, “On a stability of discontinuous particle method for transfer equation”, Math. Models Comput. Simul., 10:2 (2018), 186–197  mathnet  crossref  elib
    38. Speck J., “Finite-Time Degeneration of Hyperbolicity Without Blowup For Quasilinear Wave Equations”, Anal. PDE, 10:8 (2017), 2001–2030  crossref  isi
    39. Yu. A. Kriksin, P. A. Kuchugov, M. E. Ladonkina, O. A. Neklyudova, V. F. Tishkin, “Postroenie tochnykh reshenii nekotorykh uravnenii giperbolicheskogo tipa, soderzhaschikh razryv, rasprostranyayuschiisya po neodnorodnomu fonu”, Preprinty IPM im. M. V. Keldysha, 2018, 017, 14 pp.  mathnet  crossref
  • Успехи математических наук
    Number of views:
    This page:4345
    Full text:1568
    First page:6

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018