Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation

By Jin Cheng, J. Nakagawa, Masahiro Yamamoto, Tomohiro Yamazaki. 2009

433 citations recorded by the source corpus.

Subfields: Mathematical Physics, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/ed6363cd4f1f12c90a456d54c1e7c6204f28eb88

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Mechanics of Materials

In Modeling and Simulation

Citations in the corpus

Spectral Optimization Methods for the Time Fractional Diffusion Inverse Problem (2013, methodology): “We mention, among others, the work [3] to determine the fractional order α and variable diffusion coefficient by means of additional boundary data.”
Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems (2011, background): “As for an inverse problem of determining a coefficient and the order α in the case where the spatial dimension is one, see Cheng, Nakagawa, Yamamoto and Yamazaki [6].”
Recovering an unknown source in a fractional diffusion problem (2017, neutral): “This is severely ill-conditioned for the heat equation, but for 0 α 1 is only moderately so (equal to a 2-derivative loss) , [2].”
Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation (2014, methodology): “Similarly to [8], by means of the eigensystem {λk, φk}∞k=1, we can define the weak solution to (2), but we here omit the details.”
Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion (2013, neutral): “Thus, these useful studies do not cover the interesting case of solutions with limited regularity due to low regularity of the data, a typical case for related inverse problems; see, e.g., [5] and also [11] and [24] for its parabolic counterpart.”
A tutorial on inverse problems for anomalous diffusion processes (2015, positive): “Cheng et al [14] established the unique recovery of the fractional order α ∈ (0 , 1) and the diﬀusion coeﬃcient from the lateral boundary measurements.”
A UNIQUENESS RESULT FOR AN INVERSE PROBLEM IN A SPACE-TIME FRACTIONAL DIFFUSION EQUATION (2013, background): “Important references documenting the recent interest on inverse problems with fractional derivatives are [4, 6, 9, 10, 13, 14, 16, 17, 18].”