On the Identification of Source Term in the Heat Equation from Sparse Data

DOI10.1137/19M1279915zbMath1433.65198arXiv1908.02015OpenAlexW3014722960MaRDI QIDQ4960424

William Rundell, Zhi-Dong Zhang

Publication date: 16 April 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.02015

zbMATH Keywords

inverse problemuniquenessregularizationnonlinearitynumerical reconstructionsparse measurementsheat (diffusion) equationmultiple unknowns

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Inverse problems for PDEs (35R30) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Inverse problems in thermodynamics and heat transfer (80A23) Basic methods in thermodynamics and heat transfer (80M99)

Related Items (8)

Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements ⋮ Identification of an unknown spatial source function in a multidimensional hyperbolic partial differential equation with interior degeneracy ⋮ Logarithmic Stable Recovery of the Source and the Initial State of Time Fractional Diffusion Equations ⋮ Unique determination of fractional order and source term in a fractional diffusion equation from sparse boundary data ⋮ Inverse source problem for a space-time fractional diffusion equation ⋮ Reconstruction of a Space-Time-Dependent Source in Subdiffusion Models via a Perturbation Approach ⋮ On an inverse problem of nonlinear imaging with fractional damping ⋮ Uniqueness and numerical inversion in the time-domain fluorescence diffuse optical tomography

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