The heat equation source determination for the case of non-smooth boundary and initial conditions

5th International Conference on "Problems of Mathematical and Theoretical Physics and Mathematical Modelling"

物理学;数学

Solovi'Ev, V.V.^1 ; Tkachenko, D.S.^1

National Research Nuclear University, MEPhI (Moscow Engineering Physics Institute), 31 Kashirskoe shosse, Moscow

115409, Russia^1

关键词: Existence and uniqueness of solution;    Fredholm;    Heat equation;    Parabolic Equations;    Smooth boundary;    Source determinations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/788/1/012058/pdf
DOI  :  10.1088/1742-6596/788/1/012058

来源: IOP

【 摘 要 】

An inverse problem of reconstructing the source of a special kind for parabolic equations in a bounded region with smooth boundary is considered. Solutions are sought in the Holder classes. We prove an uniqueness criterion for the solution and sufficient conditions of Fredholm property of the task at hand. As a consequence of the sufficient conditions for existence and uniqueness of solution of the inhomogeneous inverse problems are found.