Approximate solutions of inverse problems for nonlinear space fractional diffusion equations with randomly perturbed data

Erkan Nane; Nguyen Huy Tuan

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arXiv · 1611.01876

Approximate solutions of inverse problems for nonlinear space fractional diffusion equations with randomly perturbed data

Erkan Nane·Nguyen Huy Tuan

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Abstract

This paper is concerned with backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the instable solution, we develop some new regularized method for solving the problem. In the case of constant coefficients, we use the truncation methods. In the case of perturbed time dependent coefficients, we apply a new quasi-reversibility method. We also show the convergence rate between the regularized solution and the sought solution under some a priori assumption on the sought solution.

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BibTeX RIS

Erkan Nane, Nguyen Huy Tuan. 2016-11-07. Approximate solutions of inverse problems for nonlinear space fractional diffusion equations with randomly perturbed data. https://arxiv.org/abs/1611.01876

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