Inverse source problems for positive operators. I: Hypoelliptic diffusion and subdiffusion equations

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Title: Inverse source problems for positive operators. I: Hypoelliptic diffusion and subdiffusion equations
Authors: Ruzhansky, M
Tokmagambetov, N
Torebek, BT
Item Type: Journal Article
Abstract: A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered. The results on existence and uniqueness of solutions of these problems as well as on the fractional time diffusion (subdiffusion) equations are presented. Consequently, the obtained results are applied for the similar inverse problems for a large class of subelliptic diffusion and subdiffusion equations (with continuous spectrum). Such problems are modelled by using general homogeneous left-invariant hypoelliptic operators on general graded Lie groups. A list of examples is discussed, including Sturm–Liouville problems, differential models with involution, fractional Sturm–Liouville operators, harmonic and anharmonic oscillators, Landau Hamiltonians, fractional Laplacians, and harmonic and anharmonic operators on the Heisenberg group. The rod cooling problem for the diffusion with involution is modelled numerically, showing how to find a “cooling function”, and how the involution normally slows down the cooling speed of the rod.
Issue Date: 1-Dec-2019
Date of Acceptance: 1-Oct-2019
DOI: 10.1515/jiip-2019-0031
ISSN: 0928-0219
Publisher: Walter de Gruyter GmbH
Journal / Book Title: Journal of Inverse and Ill-posed Problems
Volume: 27
Issue: 6
Copyright Statement: © 2019 The Authors. Published by De Gruyter.
Sponsor/Funder: The Leverhulme Trust
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: RPG-2017-151
Publication Status: Published
Embargo Date: 2020-10-15
Online Publication Date: 2019-10-15
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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