A BACKWARD HEAT EQUATION IN SPHERICAL COORDINATES WITH NONLINEAR HEAT SOURCE
Main Article Content
Abstract
The problem of determining the initial temperature distribution in the backward heat equation (BHP) has attracted significant attention across various physical disciplines. While numerous studies have addressed the linear version of this inverse problem, the nonlinear case remains largely unexplored. To the best of our knowledge, the literature contains only limited results regarding the nonlinear BHP formulated in spherical coordinates. Motivated by this research gap, the present work aims to analyze the nonlinear backward heat equation in spherical coordinates. We begin by examining the inherent ill-posedness of the problem and then propose a regularization strategy based on the quasi-boundary value method to obtain a stable approximate solution. Our analysis demonstrates that the regularized solution not only exhibits continuous dependence on the terminal data but also converges to the exact solution in an appropriate function space.
Keywords
Nonlinear backward heat equation, Inverse problem, Spherical coordinates, Regularization method, Quasi-boundary value method.
Article Details
References
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