Mixed value problem for nonlinear integro-differential equation with parabolic operator of higher power

被引：10

作者：

Yuldashev, T. K. ^{[1
]}

机构：

[1] SibSAU, Krasnoyarsk 660014, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2012年 / 52卷 / 01期

关键词：

parabolic operator of higher power; Fourier series; integral identity; generalized derivatives; countable system of nonlinear integral equations; method of successive approximations;

D O I：

10.1134/S0965542512010150

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the questions of one-valued solvability of mixed value problem for nonlinear integro-differential equation, consisting a parabolic operator of higher power. By the aid of Fourier series of separation variables the considering problem we can reduce to study the countable system of nonlinear integral equations, one-valued solvability of which will be proved by the method of successive approximations. The convergence of Fourier series will be studied by means of integral identity.

引用

页码：105 / 116

页数：12

共 50 条

[21] Nonlocal Boundary Value Problem for a Nonlinear Fredholm Integro-Differential Equation with Degenerate Kernel
T. K. Yuldashev
Differential Equations, 2018, 54 : 1646 - 1653
[22] Nonlocal Boundary Value Problem for a Nonlinear Fredholm Integro-Differential Equation with Degenerate Kernel
Yuldashev, T. K.
DIFFERENTIAL EQUATIONS, 2018, 54 (12) : 1646 - 1653
[23] A CAUCHY PROBLEM FOR AN INTEGRO-DIFFERENTIAL EQUATION OF PARABOLIC TYPE WITH A DELAYED ARGUMENT
OGUZTORE.MN
ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI RENDICONTI-CLASSE DI SCIENZE FISICHE-MATEMATICHE & NATURALI, 1969, 47 (1-2): : 19 - &
[24] On the stabilization of solutions of an initial-boundary value problem for a nonlinear integro-differential equation
Dzhangveladze, T. A.
Kiguradze, Z. V.
DIFFERENTIAL EQUATIONS, 2007, 43 (06) : 854 - 861
[25] One approach to solve a nonlinear boundary value problem for the Fredholm integro-differential equation
Dzhumabaev, D. S.
Mynbayeva, S. T.
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2020, 97 (01): : 27 - 36
[26] Finite difference scheme for one nonlinear parabolic integro-differential equation
Jangveladze, Temur
Kiguradze, Zurab
TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE, 2016, 170 (03) : 395 - 401
[27] Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation
G. Deligiannidis
S. Maurer
M. V. Tretyakov
BIT Numerical Mathematics, 2021, 61 : 1223 - 1269
[28] Inverse problem of determining the kernel in an integro-differential equation of parabolic type
Durdiev, D. K.
Rashidov, A. Sh.
DIFFERENTIAL EQUATIONS, 2014, 50 (01) : 110 - 116
[29] Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation
Deligiannidis, G.
Maurer, S.
Tretyakov, M. V.
BIT NUMERICAL MATHEMATICS, 2021, 61 (04) : 1223 - 1269
[30] Inverse problem of determining the kernel in an integro-differential equation of parabolic type
D. K. Durdiev
A. Sh. Rashidov
Differential Equations, 2014, 50 : 110 - 116

← 1 2 3 4 5 →