Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations

B. Eshmatov; E. Karimov

Open Mathematics (2007)

  • Volume: 5, Issue: 4, page 741-750
  • ISSN: 2391-5455

Abstract

top
In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations. The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type equations with two and three lines of changing type.

How to cite

top

B. Eshmatov, and E. Karimov. "Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations." Open Mathematics 5.4 (2007): 741-750. <http://eudml.org/doc/269250>.

@article{B2007,
abstract = {In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations. The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type equations with two and three lines of changing type.},
author = {B. Eshmatov, E. Karimov},
journal = {Open Mathematics},
keywords = {Parabolic-hyperbolic type equations; gluing conditions; boundary value problems; integral equation; ”abc” method; local and non-local boundary value problems; ``abc'' method; two and three lines of changing type},
language = {eng},
number = {4},
pages = {741-750},
title = {Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations},
url = {http://eudml.org/doc/269250},
volume = {5},
year = {2007},
}

TY - JOUR
AU - B. Eshmatov
AU - E. Karimov
TI - Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations
JO - Open Mathematics
PY - 2007
VL - 5
IS - 4
SP - 741
EP - 750
AB - In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations. The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type equations with two and three lines of changing type.
LA - eng
KW - Parabolic-hyperbolic type equations; gluing conditions; boundary value problems; integral equation; ”abc” method; local and non-local boundary value problems; ``abc'' method; two and three lines of changing type
UR - http://eudml.org/doc/269250
ER -

References

top
  1. [1] G. Bateman and A. Erdelyi: Higher transcendental functions. Bessel functions, functions of parabolic cylinder, orthogonal polynomials (in Russian), Russian translation of extracts from Volume II of the original English edition (McGraw Hill, New York, 1953), Nauka, Moscow, 1966. 
  2. [2] A.S. Berdyshev and E.T. Karimov: “Some non-local problems for the parabolich-yperbolic type equation with non-characteristic line of changing type”, Cent. Eur. J. Math., Vol. 4, (2006), no. 2, pp. 183–193. http://dx.doi.org/10.2478/s11533-006-0007-8 Zbl1098.35116
  3. [3] A. Friedman: Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. 
  4. [4] I.M. Gel’fand: “Some questions of analysis and differential equations” (in Russian), Uspehi Mat. Nauk, Vol. 14, (1959), no. 3, pp. 3–19. 
  5. [5] N.Yu. Kapustin and E.I. Moiseev: “On spectral problems with a spectral parameter in the boundary condition” (in Russian), Differ. Uravn., Vol. 33, (1997), no. 1, pp. 115–119, 143. 
  6. [6] E.T. Karimov: “About the Tricomi problem for the mixed parabolic-hyperbolic type equation with complex spectral parameter”, Complex Var. Theory Appl., Vol. 50, (2005), no. 6, pp. 433–440. Zbl1080.35048
  7. [7] E.T. Karimov: “Non-local problems with special gluing condition for the parabolichyperbolic type equation with complex spectral parameter”, Panamer. Math. J., Vol. 17, (2007), no. 2, pp. 11–20. Zbl1144.35450
  8. [8] M.L. Krasnov: Integral equations. Introduction to the theory (in Russian), Nauka, Moscow, 1975. 
  9. [9] J.M. Rassias: Lecture notes on mixed type partial differential equations, World Scientific Publishing Co., Inc., Teaneck, NJ, 1990. 
  10. [10] K.B. Sabytov: “On the theory of equations of mixed parabolic-hyperbolic type with a spectral parameter”, Differentsial’nye Uravneniya, Vol. 25, (1989), no. 1, pp. 117–126, 181–182. 
  11. [11] M.S. Salakhitdinov and A.K. Urinov: Boundary value problems for equations of mixed type with a spectral parameter (in Russian), Fan, Tashkent, 1997. 
  12. [12] A.G. Shashkov: System-structural analysis of the heat exchange proceses and its application, Moscow, 1983. 
  13. [13] G.D. Tojzhanova and M.A. Sadybekov: “Spectral properties of an analogue of the Tricomi problem for an equation of mixed parabolic-hyperbolic type” (in Russian), Izv. Akad. Nauk Kazakh. SSR Ser. Fiz.-Mat., (1990), no. 5, pp. 48–52. Zbl0728.35074

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.