On nonlinear Sobolev equations with terminal observations in \(L^p\) spaces

Authors
  • Donal O'Regan

    School of Mathematical and Statistical Sciences, University of Galway, Ireland

Keywords:
Conformable derivative, Fourier truncation method, regularization
Abstract

In this paper, we investigate the backward problem for the heat equation equipped with the time fractional conformable derivative. This problem is a generalization of the classical heat equation. We consider the problem with a nonlinear source function in a bounded domain. This problem is shown to be ill-posed, so we regularize the solution by the Fourier truncated method and we estimate the error term in the \(L^p(\mathcal{D})\) space. An example to illustrate the theory is given in the final section.

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Additional Files
Published
28-03-2025
Section
Research Article
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Copyright (c) 2023 Donal O'Regan

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How to Cite

On nonlinear Sobolev equations with terminal observations in \(L^p\) spaces. (2025). Letters on Applied and Pure Mathematics, 1(1), 30-42. https://doi.org/10.66147/lapm.20231111

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