Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type

A. Berdyshev; E. Karimov

Open Mathematics (2006)

  • Volume: 4, Issue: 2, page 183-193
  • ISSN: 2391-5455

Abstract

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In this work two non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type are considered. Unique solvability of these problems is proven. The uniqueness of the solution is proven by the method of energy integrals and the existence is proven by the method of integral equations.

How to cite

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A. Berdyshev, and E. Karimov. "Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type." Open Mathematics 4.2 (2006): 183-193. <http://eudml.org/doc/269509>.

@article{A2006,
abstract = {In this work two non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type are considered. Unique solvability of these problems is proven. The uniqueness of the solution is proven by the method of energy integrals and the existence is proven by the method of integral equations.},
author = {A. Berdyshev, E. Karimov},
journal = {Open Mathematics},
keywords = {35M10; 35P05; 35A05},
language = {eng},
number = {2},
pages = {183-193},
title = {Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type},
url = {http://eudml.org/doc/269509},
volume = {4},
year = {2006},
}

TY - JOUR
AU - A. Berdyshev
AU - E. Karimov
TI - Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type
JO - Open Mathematics
PY - 2006
VL - 4
IS - 2
SP - 183
EP - 193
AB - In this work two non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type are considered. Unique solvability of these problems is proven. The uniqueness of the solution is proven by the method of energy integrals and the existence is proven by the method of integral equations.
LA - eng
KW - 35M10; 35P05; 35A05
UR - http://eudml.org/doc/269509
ER -

References

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  8. [8] V.A. Eleev: “Analogue of the Tricomi problem for the mixed parabolic-hyperbolic equations with non-characteristic line of changing type”, Differensialniye Uravneniya, Vol. 13(1), (1977), pp. 56–63. 
  9. [9] N.Y. Kapustin: “The Tricomi problem for the parabolic-hyperbolic equation with degenerating hyperbolic part”, Differensialniye Uravneniya, Vol. 24(8), (1988), pp. 1379–1386. 
  10. [10] G.D. Tojzhanova and M.A. Sadybekov: “About spectral properties of one analogue of the Tricomi problem for the mixed parabolic-hyperbolictype equation”, Izvestija AN KazSSR, ser.phys.-math.nauk, Vol. 3, (1989), pp. 48–52. 
  11. [11] A.S. Berdyshev: “Nonlocal boundary problems for the mixed type equation in the domain with deviation from the characteristic”, Differensilaniye Uravneniya, Vol. 29(12), (1993), pp. 2118–2125. 
  12. [12] A.S. Berdyshev: “On uniqueness of the solution of general Tricomi problem for the parabolic-hyperbolic equation”, Doklady ANRUz., Vol. 10, (1994), pp. 5–7. 
  13. [13] A.N. Tikhonov and A.A. Samarskij: Equations of mathematical physics, Nauka, Moscow, 1977, p. 736. 
  14. [14] M.S. Salakhitdinov and A.K. Urinov: Boundary value problems for the mixed type equations with spectral parameter, Fan, Tashkent, 1997, p. 166. 
  15. [15] G. Bateman and A. Erdelji: Higher transcendent functions, Nauka, Moscow, 1965, p. 296. 
  16. [16] A. Fridman: Partial differential equations of parabolic type, Izdatelstvo Mir, Moscow, 1968, p. 428. 

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