INVERSE CAUCHY PROBLEM FOR FRACTIONAL TELEGRAPH EQUATION WITH DISTRIBUTIONS

被引：1

作者：

Lopushanska, H. ^{[1
]}

Rapita, V ^{[1
]}

机构：

[1] Ivan Franko Natl Univ, 1 Univ Str, UA-79000 Lvov, Ukraine

来源：

CARPATHIAN MATHEMATICAL PUBLICATIONS | 2016年 / 8卷 / 01期

关键词：

generalized function; fractional derivative; inverse problem; Green vector-function;

D O I：

10.15330/cmp.8.1.118-126

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The inverse Cauchy problem for the fractional telegraph equation u(t)((alpha)) - r(t)u(t)((beta)) + a(2)(-Delta)(gamma/2)u = F-0(x)g(t), (x,t) is an element of R-n x (0, T], with given distributions in the right- hand sides of the equation and initial conditions is studied. Our task is to determinate a pair of functions: a generalized solution u (continuous in time variable in general sense) and unknown continuous minor coefficient r(t). The unique solvability of the problem is established.

引用

页码：118 / 126

页数：9

共 50 条

[1] INVERSE SOURCE CAUCHY PROBLEM FOR A TIME FRACTIONAL DIFFUSION-WAVE EQUATION WITH DISTRIBUTIONS
Lopushansky, Andrzej
Lopushanska, Halyna
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2017,
[2] An inverse problem for the telegraph equation
Kurzhanski, AB
Sorokina, MM
[J]. SYSTEM MODELING AND OPTIMIZATION, 2005, 166 : 177 - 189
[3] ON AN INVERSE PROBLEM FOR A TELEGRAPH EQUATION
ELUBAEV, S
[J]. DOKLADY AKADEMII NAUK SSSR, 1969, 189 (03): : 461 - &
[4] INVERSE COEFFICIENT PROBLEM FOR THE SEMI-LINEAR FRACTIONAL TELEGRAPH EQUATION
Lopushanska, Halyna
Rapita, Vitalia
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[5] The cauchy problem for a higher order telegraph equation
Aleksandrovich I.M.
Sidorov M.V.
[J]. Journal of Mathematical Sciences, 2002, 109 (4) : 1680 - 1685
[6] The Uniqueness of a Solution to the Inverse Cauchy Problem for a Fractional Differential Equation in a Banach Space
Kokurin, M. M.
[J]. RUSSIAN MATHEMATICS, 2013, 57 (12) : 16 - 30
[7] On the inverse problem of the 3D telegraph equation
Chang, S
Weston, VH
[J]. INVERSE PROBLEMS, 1997, 13 (05) : 1207 - 1221
[8] Analog of the Goursat problem for a generalized fractional telegraph equation
Pshibikhova, R. A.
[J]. DIFFERENTIAL EQUATIONS, 2014, 50 (06) : 840 - 845
[9] Analog of the Goursat problem for a generalized fractional telegraph equation
R. A. Pshibikhova
[J]. Differential Equations, 2014, 50 : 840 - 845
[10] The Goursat problem for the fractional telegraph equation with Caputo derivatives
R. A. Pshibihova
[J]. Mathematical Notes, 2016, 99 : 552 - 555

← 1 2 3 4 5 →