Some non-local problems for the parabolic-hyperbolic type equation with complex spectral parameter

被引：7

作者：

Karimov, E. T. ^{[1
]}

机构：

[1] Uzbek Acad Sci, Inst Math & Informat Technol, Tashkent 125, Uzbekistan

来源：

MATHEMATISCHE NACHRICHTEN | 2008年 / 281卷 / 07期

关键词：

mixed; parabolic-hyperbolic type equations; non-local problems; spectral parameter; energy integral; integral equation;

D O I：

10.1002/mana.200510652

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper the unique solvability of two non-local problems for the mixed parabolic-hyperbolic type equation with complex spectral parameter is proved. Sectors for values of the spectral parameter where these problems have unique solutions are shown. Uniqueness of the solution is proved by the method of energy integral and existence is proved by the method of integral equations. In particular cases, eigenvalues and corresponding eigenfunctions of the studied problems are found. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.

引用

页码：959 / 970

页数：12

共 50 条

[21] On a problem of the Frankl type for an equation of the mixed parabolic-hyperbolic type
Kal'menov, Tynysbek Sh.
Sadybekov, Makhmud
INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016), 2016, 1759
[22] The inverse problem for an equation of mixed parabolic-hyperbolic type
Sabitov, K. B.
Safin, E. M.
MATHEMATICAL NOTES, 2010, 87 (5-6) : 880 - 889
[23] On some non-local problems for linear hyperbolic systems
Kiguradze, TI
DOKLADY AKADEMII NAUK, 1995, 345 (03) : 300 - 302
[24] Three-dimensional Problems for a Parabolic-Hyperbolic Equation with Two Planes of Change of Type
Islomov, B. I.
Umarova, G. B.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2020, 41 (09) : 1811 - 1822
[25] Three-dimensional Problems for a Parabolic-Hyperbolic Equation with Two Planes of Change of Type
B. I. Islomov
G. B. Umarova
Lobachevskii Journal of Mathematics, 2020, 41 : 1811 - 1822
[26] Non-local problems in time for one nonlinear parabolic equation
Shapatava, A
METMBS '05: PROCEEDINGS OF THE 2005 INTERNATIONAL CONFERENCE ON MATHEMATICS AND ENGINEERING TECHNIQUES IN MEDICINE AND BIOLOGICAL SCIENCES, 2005, : 197 - 200
[27] On a Frankl-type problem for a mixed parabolic-hyperbolic equation
T. Sh. Kal’menov
M. A. Sadybekov
Siberian Mathematical Journal, 2017, 58 : 227 - 231
[28] SPECTRAL PROPERTIES OF A FRANKL TYPE PROBLEM FOR PARABOLIC-HYPERBOLIC EQUATIONS
Sadybekov, Makhmud A.
Dildabek, Gulnar
Ivanova, Marina B.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2018,
[29] On a nonlocal boundary value problem for parabolic-hyperbolic type equation
Karahan, Done
Mamedov, Hanlar R.
NOTE DI MATEMATICA, 2023, 43 (01): : 57 - 65
[30] On a Frankl-type problem for a mixed parabolic-hyperbolic equation
Kal'menov, T. Sh.
Sadybekov, M. A.
SIBERIAN MATHEMATICAL JOURNAL, 2017, 58 (02) : 227 - 231

← 1 2 3 4 5 →