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In this work we establish log-type stability estimates for the inverse potential and conductivity problems with partial Dirichlet-to-Neumann map, where the Dirichlet data is homogeneous on the inaccessible part. This result, to some extent,…

Analysis of PDEs · Mathematics 2007-08-27 Horst Heck , Jenn-Nan Wang

In this paper, we study a nonlinear boundary diffusion equation of porous medium type arising from a boundary control problem. We give a complete and sharp characterization of the asymptotic behavior of its solutions, and prove the…

Analysis of PDEs · Mathematics 2024-02-07 Tianling Jin , Jingang Xiong , Xuzhou Yang

We give new stability estimates for the Gel'fand-Calderon inverse boundary value problem

Analysis of PDEs · Mathematics 2007-12-07 Roman Novikov

We are concerned with the Calder\'on problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the…

Analysis of PDEs · Mathematics 2019-02-13 Hongyu Liu , Chun-Hsiang Tsou

We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions $n\ge 2$. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional…

Analysis of PDEs · Mathematics 2023-09-08 Ru-Yu Lai , Lili Yan

In this paper, the robust stability and convergence to the true state of moving horizon estimator based on an adaptive arrival cost are established for nonlinear detectable systems. Robust global asymptotic stability is shown for the case…

Systems and Control · Electrical Eng. & Systems 2024-09-23 Nestor N. Deniz , Marina H. Murillo , Guido Sanchez , Lucas M. Genzelis , Leonardo Giovanini

We establish H\"older stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle from two measurements taken on the boundary of a domain…

Analysis of PDEs · Mathematics 2025-03-24 Mourad Choulli , Hiroshi Takase

We consider the inverse problem of identifying an unknown inclusion contained in an elastic body by the Dirichlet-to-Neumann map. The body is made by linearly elastic, homogeneous and isotropic material. The Lam\'e moduli of the inclusion…

Analysis of PDEs · Mathematics 2016-05-31 Giovanni Alessandrini , Michele Di Cristo , Antonino Morassi , Edi Rosset

Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…

Signal Processing · Electrical Eng. & Systems 2022-05-18 Lachlan J. Gunn , Andrew Allison , Derek Abbott

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…

Analysis of PDEs · Mathematics 2021-01-15 Gunther Uhlmann , Jian Zhai

We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…

Optimization and Control · Mathematics 2018-06-07 John Tsinias , Constantinos Kitsos

A procedure that allows study of unstable stability of a boundary layer between plasma and a magnetic field has been developed. Layer equilibrium for one reason or another is not set but follows from strict solution of kinetic equation with…

Plasma Physics · Physics 2010-05-25 V. V. Lyahov , V. M. Neshchadim

We prove a stability result in the hybrid inverse problem of recovering the electrical conductivity from partial knowledge of one current density field generated inside a body by an imposed boundary voltage. The region where interior data…

Mathematical Physics · Physics 2016-02-17 Carlos Montalto , Alexandru Tamasan

This paper considers a class of nonlinear time harmonic Maxwell systems at fixed frequency, with nonlinear terms taking the form $\mathscr{X}(x,|\vec E(x)|^2)\vec E(x)$, $\mathscr{Y}(x,|\vec H(x)|^2)\vec H(x)$, such that $\mathscr{X}(x,s)$,…

Analysis of PDEs · Mathematics 2018-04-26 Cătălin I. Cârstea

In this article, we consider the problem of finding the support of an inhomogenous possibly anisotropic inclusion in a background of constant electric conductivity from the electrical impedance tomography data at the boundary of a bounded…

Functional Analysis · Mathematics 2007-05-23 Erkki J. Somersalo

In this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half…

Analysis of PDEs · Mathematics 2015-06-03 Anupam Pal Choudhury , Venkateswaran P. Krishnan

We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain $\Omega\subset\mathbb{R}^n$ and we show that a…

Analysis of PDEs · Mathematics 2016-11-03 Giovanni Alessandrini , Maarten V. de Hoop , Romina Gaburro , Eva Sincich

We study an inverse source problem for a semilinear parabolic equation in a bounded domain, where the nonlinearity depends on the unknown function and its gradient through a quadratic reaction term and a Burgers-type convection term. From…

Analysis of PDEs · Mathematics 2026-01-22 Hu Xirui

In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…

Analysis of PDEs · Mathematics 2015-05-28 Kais Ammari , Mourad Choulli

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…

Dynamical Systems · Mathematics 2020-12-29 Mark A. Pinsky