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

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