Inverse problem of determining the right-hand side of a one-dimensional fractional diffusion equation with variable coefficients

2024/11/12 by D. K. Durdiev, Durdiev, D. K. · 2 citations
Mathematics · #Fractional Differential Equations Solutions #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.2411.08922

Abstract

In this paper, we study the inverse problem of finding a time-dependent multiplier of the right-hand side of a time-fractional one-dimensional diffusion equation with variables coefficients in the case where the usual Cauchy, homogeneous Dirichlet boundary, and an integral overdetermination conditions are given. The overdetermination condition has the form of an integral with a weight over a spatial segment from the solution of the direct problem, in which the weight function is a spatially dependent known factor of the right-hand side of the equation. This made it possible to construct a solution to the inverse problem in explicit form and prove its correctness in the class of regular solutions

Cited by

• Numerical Approaches for Identifying the Time-Dependent Potential Coefficient in the Diffusion Equation
• Numerical Identification of a Time-Dependent Coefficient in a Time-Fractional Diffusion Equation with Integral Constraints

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