一类具有非局部条件的抛物型积分微分方程的核确定问题

IF 0.6 Q3 MATHEMATICS
D.Q. Durdiev, J. J. Jumaev, D. Atoev
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引用次数: 1

摘要

研究了具有非局部初始边界和积分超定条件的一维积分微分热方程的反问题。我们使用傅里叶方法和Schauder原理来研究直接问题的可解性。进一步,将问题简化为一个关于未知函数的等效封闭积分方程组。利用压缩映射证明了积分方程解的存在唯一性。最后,利用等效性,得到经典解的存在唯一性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition
In this paper, an inverse problem for a one-dimensional integro-differential heat equation is investigated with nonlocal initial-boundary and integral overdetermination conditions. We use the Fourier method and the Schauder principle to investigate the solvability of the direct problem. Further, the problem is reduced to an equivalent closed system of integral equations with respect to unknown functions. Existence and uniqueness of the solution of the integral equations are proved using a contractive mapping. Finally, using the equivalency, the existence and uniqueness of the classical solution is obtained.
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来源期刊
CiteScore
1.20
自引率
40.00%
发文量
27
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