Conformal mapping for cavity inverse problem: an explicit reconstruction formula
From MaRDI portal
Publication:2965790
DOI10.1080/00036811.2016.1208816zbMath1361.30013arXiv1509.02693OpenAlexW2225465033WikidataQ58256251 ScholiaQ58256251MaRDI QIDQ2965790
Alexandre Munnier, Karim Ramdani
Publication date: 3 March 2017
Published in: SIAM Journal on Mathematical Analysis, Applicable Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1509.02693
cuspconformal mappingintegral equationsLaplace equationfluid-structure interactioncollisioninverse conductivity problemDirichlet-Neumann
Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with fluid mechanics (35Q35) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Asymptotic expansions of solutions to PDEs (35C20) Variational methods for second-order elliptic equations (35J20) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Schwarz-Christoffel-type mappings (30C30) Boundary value and inverse problems for harmonic functions in two dimensions (31A25) Inverse problems for integral equations (45Q05) Blow-up in context of PDEs (35B44)
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Cites Work
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- Reconstruction of inhomogeneous conductivities via the concept of generalized polarization tensors
- A quasi-reversibility approach to solve the inverse obstacle problem
- Dirichlet problem in domains with thin bridges
- A direct boundary integral equation method for transmission problems
- Elliptic boundary-value problems in domains of the exterior-of-a-cusp type
- Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid
- Dirichlet and Neumann exterior problems for the \(n\)-dimensional Laplace operator. An approach in weighted Sobolev spaces
- Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Vol. I. Transl. from the German by Georg Heinig and Christian Posthoff
- Boundary value problems in domains with cuspidal points
- Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence
- Asymptotics of the solution of the Dirichlet problem in domains with a thin crosspiece
- Dirichlet problem for elliptic equations of the second order in a singular domain of R\(^2\)
- Inverse Dirichlet problem and conformal mapping
- Reconstruction of small inhomogeneities from boundary measurements
- Generalized polarization tensors for shape description
- The ``exterior approach to solve the inverse obstacle problem for the Stokes system
- Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks
- Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain
- Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp
- Lipschitz stability for the inverse conductivity problem
- Exponential instability in an inverse problem for the Schrödinger equation
- Computation of the drag force on a sphere close to a wall
- Inverse problems and conformal mapping
- Imaging by Modification: Numerical Reconstruction of Local Conductivities from Corresponding Power Density Measurements
- Numerical Approximation Methods for Elliptic Boundary Value Problems
- Conformal mapping and an inverse impedance boundary value problem
- Conformal mapping and impedance tomography
- A Numerical Study of the Probe Method
- Uniqueness for the determination of unknown boundary and impedance with the homogeneous Robin condition
- Collisions in Three-Dimensional Fluid Structure Interaction Problems
- A stream-function-vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces
- Reconstruction of the shape of the inclusion by boundary measurements
- Recent progress in electrical impedance tomography
- On reconstruction in the inverse conductivity problem with one measurement
- Numerical implementation of two noniterative methods for locating inclusions by impedance tomography
- Numerical method for finding the convex hull of an inclusion in conductivity from boundary measurements
- The factorization method for a class of inverse elliptic problems
- Electrical impedance tomography
- Electrostatic imaging via conformal mapping
- Generic Controllability of 3D Swimmers in a Perfect Fluid
- Construction of conformal mappings by generalized polarization tensors
- A survey on sampling and probe methods for inverse problems
- A conformal mapping method in inverse obstacle scattering
- Lack of Collision Between Solid Bodies in a 2D Incompressible Viscous Flow
- Conformal mappings and inverse boundary value problems
- LACK OF COLLISION IN A SIMPLIFIED 1D MODEL FOR FLUID–SOLID INTERACTION
- On the slow motion generated in a viscous fluid by the approach of a sphere to a plane wall or stationary sphere
- Nonlinear integral equations and the iterative solution for an inverse boundary value problem
- Optimal stability for the inverse problem of multiple cavities
