On finding a cavity in a thermoelastic body using a single displacement measurement over a finite time interval on the surface of the body

DOI10.1515/jiip-2017-0066zbMath1388.74056arXiv1706.02453OpenAlexW2624228712MaRDI QIDQ1637470

Masaru Ikehata

Publication date: 8 June 2018

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.02453

zbMATH Keywords

cavitycoupled systemenclosure methodinverse obstacle problemnon-destructive testingcoupled heat equationdisplacement-temperature equation of motiondynamic theory of thermoelasticity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Thermal effects in solid mechanics (74F05) Heat equation (35K05) Inverse problems for PDEs (35R30) Wave equation (35L05) Inverse problems for waves in solid mechanics (74J25) PDEs in connection with mechanics of deformable solids (35Q74) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (9)

Finite element method for the reconstruction of a time-dependent heat source in isotropic thermoelasticity systems of type-III ⋮ The enclosure method for inverse obstacle scattering over a finite time interval. VI: Using shell-type initial data ⋮ On finding a penetrable obstacle using a single electromagnetic wave in the time domain ⋮ Extracting discontinuity using the probe and enclosure methods ⋮ The enclosure method for the detection of variable order in fractional diffusion equations ⋮ Quench Detection on a Superconducting Radio-Frequency Cavity ⋮ Prescribing a heat flux coming from a wave equation ⋮ The enclosure method for the heat equation using time-reversal invariance for a wave equation ⋮ Uniqueness for inverse source problems of determining a space-dependent source in thermoelastic systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain
• On finding an obstacle with the Leontovich boundary condition via the time domain enclosure method
• On the Neumann problem for some linear hyperbolic systems of second order
• On the Neumann problem of linear hyperbolic-parabolic coupled systems
• The enclosure method for inverse obstacle scattering over a finite time interval: IV. extraction from a single point on the graph of the response operator
• An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method
• Mixed problems for hyperbolic equations of second order
• On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity
• Reconstruction of the support function for inclusion from boundary measurements
• The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval: III. Sound-soft obstacle and bistatic data
• The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval: II. Obstacles with a dissipative boundary or finite refractive index and back-scattering data
• A remark on finding the coefficient of the dissipative boundary condition via the enclosure method in the time domain
• The framework of the enclosure method with dynamical data and its applications
• An inverse acoustic scattering problem inside a cavity with dynamical back-scattering data
• On finding an obstacle embedded in the rough background medium via the enclosure method in the time domain
• The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval
• Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data
• On reconstruction of a cavity in a linearized viscoelastic body from infinitely many transient boundary data
• On the reconstruction of inclusions in a heat conductive body from dynamical boundary data over a finite time interval
• The enclosure method for the heat equation
• Extracting the geometry of an obstacle and a zeroth-order coefficient of a boundary condition via the enclosure method using a single reflected wave over a finite time interval
• Extracting discontinuity in a heat conductive body. One-space dimensional case

This page was built for publication: On finding a cavity in a thermoelastic body using a single displacement measurement over a finite time interval on the surface of the body