A gradient-based approach for identification of the zeroth-order coefficient \(p(x)\) in the parabolic equation \(u_t=(k(x)u_x)_x-p(x)u\) from Dirichlet-type measured output
DOI10.1515/JIIP-2018-0043zbMath1420.35465OpenAlexW2934863158MaRDI QIDQ2422500
Publication date: 19 June 2019
Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/jiip-2018-0043
diffusion equationill-posednessFréchet gradientgradient formulainverse coefficient problemLipschitz continuity of the input-output operator
Fréchet and Gateaux differentiability in optimization (49J50) Initial-boundary value problems for second-order parabolic equations (35K20) Inverse problems for PDEs (35R30) Weak solutions to PDEs (35D30)
Cites Work
- Unnamed Item
- Unnamed Item
- An introduction to inverse elliptic and parabolic problems
- Lipschitz continuity of the Fréchet gradient in an inverse coefficient problem for a parabolic equation with Dirichlet measured output
- Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. application to the determination of a nonlinear term
- Applied functional analysis. Main principles and their applications
- Stability of the determination of a time-dependent coefficient in parabolic equations
- Regularization approaches for quantitative photoacoustic tomography using the radiative transfer equation
- A globally convergent numerical method for a coefficient inverse problem for a parabolic equation
- A gradient descent method for solving an inverse coefficient heat conduction problem
- Some stability estimates in determining sources and coefficients
- An Inverse Problem for a Nonlinear Diffusion Equation
- An inverse problem for a semilinear parabolic equation
- Monotonicity and Invertibility of Coefficient-to-Data Mappings for Parabolic Inverse Problems
- Introduction to Inverse Problems for Differential Equations
- An adjoint problem approach and coarse-fine mesh method for identification of the diffusion coefficient in a linear parabolic equation
- Inverse problems for partial differential equations
- An inverse problem for the heat equation
This page was built for publication: A gradient-based approach for identification of the zeroth-order coefficient \(p(x)\) in the parabolic equation \(u_t=(k(x)u_x)_x-p(x)u\) from Dirichlet-type measured output
