About Dirichlet boundary value problem for the heat equation in the infinite angular domain

Boundary value problems

Minzilya Kosmakova¹  Murat Ramazanov²  Muvasharkhan he Jenaliyev³  Meiramkul Amangaliyeva³ 

[1] Al-Farabi Kazakh National University, Almaty, Kazakhstan;E.A. Buketov Karaganda State University, Karaganda, Kazakhstan;Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

关键词: unique classes;    heat conductivity;    angular domain;    boundary value problem;    non-trivial solution;    Volterra integral equation;   

DOI  :  10.1186/s13661-014-0213-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper it is established that in an infinite angular domain for Dirichlet problem of the heat conduction equation the unique (up to a constant factor) non-trivial solution exists, which does not belong to the class of summable functions with the found weight. It is shown that for the adjoint boundary value problem the unique (up to a constant factor) non-trivial solution exists, which belongs to the class of essentially bounded functions with the weight found in the work. It is proved that the operator of a boundary value problem of heat conductivity in an infinite angular domain in a class of growing functions is Noetherian with an index which is equal to minus one. MSC: 35D05, 35K20, 45D05.

【 授权许可】

CC BY