Inverse problems for a generalized subdiffusion equation with final overdetermination

• Main Authors: Nataliia Kinash, Jaan Janno
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2019-03-01
• Series: Mathematical Modelling and Analysis
• Subjects: inverse problem; subdiffusion; final overdetermination; fractional diffusion
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/6726

We consider two inverse problems for a generalized subdiffusion equation that use the final overdetermination condition. Firstly, we study a problem of reconstruction of a specific space-dependent component in a source term. We prove existence, uniqueness and stability of the solution to this problem. Based on these results, we consider an inverse problem of identification of a space-dependent coefficient of a linear reaction term. We prove the uniqueness and local existence and stability of the solution to this problem.