Unique determination of fractional order and source term in a fractional diffusion equation from sparse boundary data
Zhiyuan Li, Zhidong Zhang
Abstract
Abstract In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By using a sequence of harmonic functions, we construct useful quantitative relation between the unknowns and measurements. From Laplace transform and the knowledge in complex analysis, the uniqueness theorem is proved.
Topics & Concepts
MathematicsLaplace transformUniquenessTerm (time)Mathematical analysisInverse problemOrder (exchange)Applied mathematicsSequence (biology)Boundary (topology)InverseFractional calculusInverse Laplace transformBoundary value problemDiffusionHarmonicUniqueness theorem for Poisson's equationDiffusion equationConstruct (python library)Third orderHarmonic functionLaplace–Stieltjes transformType (biology)Numerical methods in inverse problemsFractional Differential Equations SolutionsDifferential Equations and Boundary Problems