Simultaneous uniqueness for multiple parameters identification in a fractional diffusion-wave equation

DOI10.3934/ipi.2022019zbMath1497.35517arXiv2103.07720OpenAlexW3136599486MaRDI QIDQ2674901

Masahiro Yamamoto, Xiaohua Jing

Publication date: 14 September 2022

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.07720

zbMATH Keywords

inverse problemuniquenesstime-fractional diffusion equationmultiple parameterstime-fractional wave equation

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Initial-boundary value problems for second-order parabolic equations (35K20) Inverse problems for PDEs (35R30) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Uniqueness for an inverse coefficient problem for a one-dimensional time-fractional diffusion equation with non-zero boundary conditions ⋮ Recovery of multiple parameters in subdiffusion from one lateral boundary measurement ⋮ Reconstruction and stability analysis of potential appearing in time‐fractional subdiffusion

Cites Work

• Unnamed Item
• Unnamed Item
• Strong maximum principle for fractional diffusion equations and an application to an inverse source problem
• Identification of the zeroth-order coefficient in a time fractional diffusion equation
• Harnack's inequality for a space-time fractional diffusion equation and applications to an inverse source problem
• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• Simultaneously recovering potentials and embedded obstacles for anisotropic fractional Schrödinger operators
• Uniqueness and nonuniqueness in an inverse problem for the parabolic equation
• A uniqueness theorem in an identification problem for coefficients of parabolic equations
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• On time-fractional diffusion equations with space-dependent variable order
• Weak solutions to non-homogeneous boundary value problems for time-fractional diffusion equations
• Simultaneous inversion of the fractional order and the space-dependent source term for the time-fractional diffusion equation
• Uniqueness for identifying a space-dependent zeroth-order coefficient in a time-fractional diffusion-wave equation from a single boundary point measurement
• Determining a fractional Helmholtz equation with unknown source and scattering potential
• The backward problem of parabolic equations with the measurements on a discrete set
• Uniqueness in inverse boundary value problems for fractional diffusion equations
• An inverse time-dependent source problem for a time-fractional diffusion equation
• Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation
• Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation
• Coefficient inverse problem for a fractional diffusion equation
• An inverse problem for a one-dimensional time-fractional diffusion problem
• FRACTIONAL DIFFUSIVE WAVES
• Inverse source problem for a fractional diffusion equation
• Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation
• Reconstruction of an order of derivative and a source term in a fractional diffusion equation from final measurements
• Fractional Differential Equations
• Recovering the potential and order in one-dimensional time-fractional diffusion with unknown initial condition and source ^*
• Reconstruction of the temporal component in the source term of a (time-fractional) diffusion equation
• Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation
• Inverse moving source problem for time-fractional evolution equations: determination of profiles
• Uniqueness in determining fractional orders of derivatives and initial values
• Identifying a fractional order and a space source term in a time-fractional diffusion-wave equation simultaneously
• A tutorial on inverse problems for anomalous diffusion processes
• Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations
• Simultaneous inversion of the potential term and the fractional orders in a multi-term time-fractional diffusion equation
• The random walk's guide to anomalous diffusion: A fractional dynamics approach
• Simultaneous inversion of two initial values for a time‐fractional diffusion‐wave equation