Related papers: An inverse Signorini obstacle problem
Now a final and maybe simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a {\it spacial domain with an outer boundary} over a finite time interval is fixed. The…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
In this paper, we give a positive answer to a longstanding open problem for determining the shape of an obstacle from the knowledge of the far field pattern for the scattering of time-harmonic elastic wave. We show that the elastic far…
A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide…
In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…
We prove under general assumptions that solutions of the thin obstacle or Signorini problem in any space dimension achieve the optimal regularity $C^{1,1/2}$. This improves the known optimal regularity results by allowing the thin obstacle…
For an initial-boundary value problem for a parabolic equation in the spatial variable $x=(x_1,.., x_n)$ and time $t$, we consider an inverse problem of determining a coefficient which is independent of one spatial component $x_n$ by extra…
This article proposes a boundary element method for the dynamic contact between a linearly elastic body and a rigid obstacle. The Signorini contact problem is formulated as a variational inequality for the Poincar\'{e}-Steklov operator for…
In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…
We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…
The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian.…
We obtain explicit estimates on the stability of the unique continuation for a linear system of hyperbolic equations. In particular our result applies to the elasticity system and also the Maxwell system. As an application, we study the…
We prove an epiperimetric inequality for the thin obstacle problem, extending the pioneering results by Weiss on the classical obstacle problem (Invent. Math. 138 (1999), no. 1, 23-50). This inequality provides the means to study the rate…
We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic…
We consider elliptic variational inequalities generated by obstacle type problems with thin obstacles. For this class of problems, we deduce estimates of the distance (measured in terms of the natural energy norm) between the exact solution…
We derive a new residual-type a posteriori estimator for a singularly perturbed reaction-diffusion problem with obstacle constraints. It generalizes robust residual estimators for unconstrained singularly perturbed equations. Upper and…
The dependence of the elastic tensor on the equilibrium stress is investigated theoretically. Using ideas from finite-elasticity, it is first shown that both the equilibrium stress and elastic tensor are given uniquely in terms of the…
We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [de Hoop, Uhlmann, Wang. Math. Ann. (2019) doi:10.1007/s00208-018-01796-y]. We show that all the parameters appearing in the equation…
We prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based…
In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…