Browse > Article
http://dx.doi.org/10.11568/kjm.2011.19.2.111

TRICOMI PROBLEM FOR THE ELLIPTIC-HYPERBOLIC EQUATION OF THE SECOND KIND  

Salahitdinov, M.S. (Institute of Mathematics and information technology of Academy Science of the Republic of Uzbekistan)
Mamadaliev, N.K. (National University of Uzbekistan)
Publication Information
Korean Journal of Mathematics / v.19, no.2, 2011 , pp. 111-127 More about this Journal
Abstract
We prove the uniqueness solvability of the Tricomi problem for the elliptic - hyperbolical equation of the second type by using a new representation of the solution in the generalized class R.
Keywords
Tricomi problem; elliptic - hyperbolic equation of the second type; line of parabolic degeneration; conditions of the splicing; marginal problems;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Babenko K.I., To the theory of the mixed-type equations, PhD thesis (1951).
2 Beryozin S.I., About Cauchy problem for linear equation of the second order with initial conditions on parabolic line, Math. collection., 24 (1949), 301-320.
3 Bicadze. A.V., Liner mixed-type differential equations with partial derivatives, Reports AS USSR 3 (1958), 36-42.
4 Bicadze. A.V., Equations of the mixed type. Moscow, (1959).
5 Eleev. V.A, About some problems of Cauchy problem type with shift for one degenerate hyperbolic equation, J. Differential equations. 12(1) (1976), 46-58.
6 Frankl F.I. , About Cauchy problem for the mixed equation of elliptic - hyperbolical type with initial conditions on transient line, lime of AS USSR, series. mathematica, 8(5) (1945), 195-224.
7 Gellstedt S., Boundary value problem for the linear equation the second order of the mixed type of the second kind, Upsala (1935).
8 Gellstedt S., About a one boundary problem for the equation $y^{2s}z_{xx}$ + $z_{yy}$ = 0, Archive Math., Astronomy and Physics, 25A(10) (1935), 1-12.
9 Gellerstedt S., Solution of mixed problem's for equation $y^mz_{xx}$ +$z_{yy}$ , Archive Math., Astronomy and Physics, 26A(3) (1936), 1-32.
10 Gellerstedt S., About linear equation second order of the mixed type, Archive Math., Astronomy and Physics, 25A(29) (1937), 1-23.
11 Germain P., Bader R., Problem of Trikomi, Reports AS Paris, 232 (1951), 463- 465.
12 Helwig G., About a partial differential equation of second order of the mixed type, Mathematical Notes, 61 (1954), 26-46.
13 Holmgren E., About a one boundary problem for the equation $y^mz_{xx}$ +$ z_{yy} $= 0, Archive for Math., Astronomy and Physics, 19(14) (1926), 1-3.
14 Isamuhamedov S.S., Modified Tricomi problem for the mixed-type equation of the second kind, Collection of works "Boundary value problems for differential equations". Tashkent, (1971).
15 Karol, I.L., On a boundary value problem for the mixed elliptic-hyperbolic equation, Report of AS USSR, 88(2) (1953), 197-200.
16 Okunev L.Ya., Hight algebra. Moscow, (1958).
17 Keldish M.V., On some accident degenerates of the elliptical equations on boundary of domain Reports AS USSR, 77(2) (1951), 181-183.
18 Mamadaliev, N.K., Non-local problems for parabolic-hyperbolic equation, Uzbek Math. Journal 5 (1991), 37-44.
19 Mamadaliev, N.K., Representation of a solution to modified Cauchy Problem, Siberian Math. Journal, 41(5) (2000), 1087-1097.
20 Oleinik O.A., About equations of elliptical type which degenerated on boundary of domain Reports AS USSR, 87(6) (1952), 885-887.
21 Protter M.H., The Cauchy problem for a hyperbolic second order equation, J. of Math., 6(4) (1954), 542-553.
22 Prudnikov, A.P., Brychkov Yu.A. and Marichev O.I., Integrals and Series. Special Functions, Moscow, (1983).
23 Smirnov M.M., Equations of mixed type. Moscow, (1970).
24 Tersenov, S.A., To the theory of hyperbolic equations with facts on the line of degeneration type, Siberian Mathematical Journal, 2(6) (1961), 913-935.
25 Tricomi F., About liner mixed-type equations, Moskow (1947).