Related papers: A parabolic inverse problem with mixed boundary da…
In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we solve two inverse problems for stochastic parabolic equations. One is concerned with a determination problem of the…
Boundary value problems for the nonlinear Schrodinger equation on the half line in laboratory coordinates are considered. A class of boundary conditions that lead to linearizable problems is identified by introducing appropriate extensions…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
Input-to-state stability (ISS) for systems described by partial differential equations has seen intensified research activity recently, and in particular the class of boundary control systems, for which truly infinite-dimensional effects…
We investigate the properties of certain elliptic systems leading, a~priori, to solutions that belong to the space of Radon measures. We show that if the problem is equipped with a so-called asymptotic Uhlenbeck structure, then the solution…
We establish various uniqueness results for inverse spectral problems of Sturm-Liouville operators with a finite number of discontinuities at interior points at which we impose the usual transmission conditions. We consider both the case of…
The analytical solution of the equation describing diffusion of intrinsic point defects has been obtained for a one-dimensional finite-length domain. This solution is intended for investigating and modeling the changes in defect…
We study the inverse Robin problem for the Schr\"odinger equation in a half-space. The potential is assumed to be compactly supported. We first solve the direct problem for dimensions two and three. We then show that the Robin-to-Robin map…
The classical Calder\'on problem with partial data is known to be log-log stable in some special cases, but even the uniqueness problem is open in general. We study the partial data stability of an analogous inverse fractional conductivity…
An isoperimetric upper bound on the resistance is given. As a corollary we resolve two problems, regarding mean commute time on finite graphs and resistance on percolation clusters. Further conjectures are presented.
In this paper, we establish a global Carleman estimate for an Ultrahyperbolic Schr\"odinger equation. Moreover, we prove H\"older stability for the inverse problem of determining a coefficient or a source term in the Ultrahyperbolic…
In this article we establish the well-posedness, energy estimates, stability, and local null controllability for the thermistor system modeled by a parabolic-parabolic system using a control force acting on just one equation of the system.…
The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…
The size estimation problem in electrical impedance tomography is considered when the conductivity is a complex number and the body is two-dimensional. Upper and lower bounds on the volume fraction of the unknown inclusion embedded in the…
We consider parabolic systems with nonlinear dynamic boundary conditions, for which we give a rigorous derivation. Then, we give them several physical interpretations which includes an interpretation for the porous-medium equation, and for…
We consider the inverse conductivity problem of identifying embedded objects in unbounded domains. The main tool is a set of special solutions to the Schroedinger equation, the complex spherical waves, which are constructed by a Carleman…
We consider a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with emphasis on rough interfaces which bear a fractal-like geometry and nonlinear dynamic (possibly, nonlocal)\ boundary…
This paper is devoted to the inverse problem of recovering the unknown distributed flux on an inaccessible part of boundary using measurement data on the accessible part. We establish and verify a variational source condition for this…
Coulomb repulsion is taken into account to derive the thermodynamics of charged bosons in a random external potential. A simple analytical form of the partition function is proposed for the case of non-overlapping localised states (i.e. a…
The global static stability of a Starling Resistor conveying non-Newtonian fluid is considered. The Starling Resistor consists of two rigid circular tubes and axisymmetric collapsible tube mounted between them. Upstream and downstream…