Direct and Inverse Problems for the Heat Equation with a Dynamic type Boundary Condition

2013/06/20 by Н. Б. Керимов, Nazim B. Kerimov, Kerimov, Nazim B. +2
Computer Science · Mathematics · Physics and Astronomy · #34B09 #35K05 #35K20 #35R30 #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #advanced mathematical theories #math-ph #math.MP #msc:34B09 #msc:35K05 #msc:35K20 #msc:35R30

paper · pdf · doi:10.48550/arxiv.1306.4772

arxiv created 2013/06/20 · openalex publication_date 2013/06/20 · arxiv updated 2013/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers the initial-boundary value problem for the heat equation with a dynamic type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon the data of the classical solution are shown by using the generalized Fourier method. This paper also investigates the inverse problem of finding a time-dependent coefficient of the heat equation from the data of integral overdetermination condition.

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