Inverse Problems of Fractional Diffusion Equations

Yong Zhou
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Yong Zhou: Macau University of Science and Technology, Macao Centre for Mathematical Sciences

Chapter Chapter 3 in Fractional Diffusion and Wave Equations, 2024, pp 81-150 from Springer

Abstract: Abstract This chapter deals with the inverse problems of time fractional diffusion equationsfractional diffusion equation(s) of order α ∈ ( 0 , 1 ) $$\alpha \in (0,1)$$ . In Sect. 3.1, we study a backward problembackward problem for an inhomogeneous fractional diffusion equationfractional diffusion equation(s) in a bounded domain. By applying the properties of the Mittag-Leffler functionsMittag-Leffler function(s) and the method of eigenvalue expansion, we establish some results about the existenceexistence, uniquenessuniqueness, and regularityregularity of the mild solutionsmild solution(s) and the classical solutionsclassical solution of the proposed problem in a weighted Hölder continuous function space. In Sect. 3.2, we consider a final value problemfinal value problem(s) for a diffusion equation with time-space fractional differentiation on a bounded domain D of ℝ k $$ \mathbb {R}^{k}$$ , k ≥ 1 $$k\ge 1$$ , which includes the fractional power L β $$\mathscr {L}^\beta $$ , 0

Date: 2024
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DOI: 10.1007/978-3-031-74031-2_3

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