Skip to main content
Log in

On solution of the fundamental boundary value problems for a one-dimensional parabolic equation of second order by the method of potentials

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. M. Gevrey, “Sur les équations aux derivées partielles du type parabolique,” J. Math. Pures et Appl.,9, No. 1-4, 305–471 (1913).

    Google Scholar 

  2. L. I. Kamynin, “On the smoothness of heat potentials,” I, Differents. Uravneniya,1, No. 6, 799–839 (1965).

    Google Scholar 

  3. L. I. Kamynin, “On the smoothness of heat potentials,” II, Differents. Uravneniya,2, No. 5, 647–687 (1966).

    Google Scholar 

  4. L. I. Kamynin, “On the smoothness of heat potentials,” III, Differents. Uravneniya,2, No. 10, 1333–1357 (1966);2, No. 11, 1484–1501 (1966).

    Google Scholar 

  5. L. I. Kamynin, “On the smoothness of heat potentials,” IV, Differents. Uravneniya,3, No. 6, 948–964 (1967);3, No. 8, 1303–1312 (1967).

    Google Scholar 

  6. L. I. Kamynin, “On the smoothness of heat potentials,” V, Differents. Uravneniya,4, No. 2, 347–365 (1968);4, No. 5, 881–895 (1968).

    Google Scholar 

  7. L. I. Kamynin, “On the smoothness of heat potentials,” VI, Differents. Uravneniya,4, No. 10, 1867–1891 (1968);4, No. 11, 2034–2055 (1968).

    Google Scholar 

  8. L. I. Kamynin, “On the smoothness of heat potentials in Dini-Hölder space,“ Sibirsk. Matem. Zh.,11, No. 5, 1017–1045 (1970).

    Google Scholar 

  9. W. Pogorzelski, “Étude de la solution fondamentale de l'équation parabolique,” Ric. Mat.,5, No. 1, 25–57 (1956).

    Google Scholar 

  10. A. M. Il'in, A. S. Kalashnikov, and O. A. Oleinik, “Linear second order parabolic equations,” Uspekhi Matem. Nauk,17, No. 3 (105), 3–146 (1962).

    Google Scholar 

  11. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasi-Linear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  12. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall (1964).

  13. L. I. Kamynin, “On Gevrey's theory for parabolic potentials,” I, Differents. Uravneniya,7, No. 2, 312–328 (1971).

    Google Scholar 

  14. L. I. Kamynin, “On Gevrey's theory for parabolic potentials,” II. Differents. Uravneniya,7, No. 4, 711–726 (1971).

    Google Scholar 

  15. L. I. Kamynin, “On Gevrey's theory for parabolic potentials,” III, Differents. Uravneniya,7, No. 8, 1473–1489 (1971).

    Google Scholar 

  16. L. I. Kamynin, “On Gevrey's theory for parabolic potentials,” IV, Differents. Uravneniya,8, No. 2, 318–332 (1972).

    Google Scholar 

  17. L. I. Kamynin, “On Gevrey's theory for parabolic potentials,” V, Differents. Uravneniya,8, No. 3, 494–509 (1972).

    Google Scholar 

  18. L. I. Kamynin, “On Gevrey's theory for parabolic potentials,” VI, Differents. Uravneniya,8, No. 6, 1015–1025 (1972).

    Google Scholar 

  19. M. I. Matiichuk and S. D. Eidel'man, “On parabolic systems with coefficients satisfving a Dini condition,” Dokl. AN SSSR,165, No. 3, 482–485 (1965).

    Google Scholar 

  20. M. I. Matiichuk and S. D. Eidel'man, “On the fundamental solutions and the Cauchy problem for parabolic systems, whose coefficients satisfy a Dini condition,” Tr. Seminara po Funktsional'nomu Analizu, No. 9, 54–83, Voronezh (1967).

    Google Scholar 

  21. R. Vyborny, “On the properties of the solutions of some boundary value problems for equations of parabolic type,” Dokl. AN SSSR,117, No. 4, 563–565 (1957).

    Google Scholar 

  22. L. I. Kamynin and B. N. Khimchenko, “On the maximum principle for parabolic 2nd order equations,” Dokl. AN SSSR,200, No. 2, 282–285 (1971).

    Google Scholar 

  23. L. I. Kamynin and B. N. Khimchenko, “On the maximum principle for elliptic-parabolic 2nd order equations,” Sibirsk. Matem. Zh.,13, No. 4, 773–789 (1972).

    Google Scholar 

  24. L. I. Kamynin and B. N. Khimchenko, “On applications of the maximum principle to parabolic 2nd order equations,” Dokl. AN SSSR,204, No. 3, 529–532 (1972).

    Google Scholar 

  25. L. I. Kamynin and B. N. Khimchenko, “On analogs of Gireaux's theorem for parabolic equations of the second order,” Sibirsk. Matem. Zh.,14, No. 1, 86–110 (1973).

    Google Scholar 

  26. A. F. Timan, Theory of Approximation of Functions of a Real Variable [in Russian], GIFML, Moscow (1960).

    Google Scholar 

  27. A. N. Tikhonov, “Uniqueness theorems for the equation of heat conduction,” Matem. Sb.,42, No. 2, 199–216 (1935).

    Google Scholar 

  28. E. A. Baderko, “On the solution of a problem of heat conduction with concentrated heat capacities by the method of parabolic potentials,” Differents. Uravneniya,8, No. 7, 1225–1234 (1972).

    Google Scholar 

  29. L. I. Kamynin, “The method of heat potentials for a parabolic equation with discontinuous coefficients,” Sibirsk. Matem. Zh.,4, No. 5, 1075–1110 (1963).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 15, No. 4, pp. 806–834, July–August, 1974.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kamynin, L.I. On solution of the fundamental boundary value problems for a one-dimensional parabolic equation of second order by the method of potentials. Sib Math J 15, 573–592 (1974). https://doi.org/10.1007/BF00967433

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00967433

Keywords

Navigation