Related papers: Notes on unique continuation properties for Partia…
We establish both Lipschitz and logarithmic stability estimates for an inverse flux problem and subsequently apply these results to an inverse boundary coefficient problem. Furthermore, we demonstrate how the stability inequalities derived…
The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in…
We consider a slow diffusion equation with a singular quenching term, extending the mathematical treatment made in 1992 by B. Kawohl and R. Kersner for the one-dimensional case. Besides the existence of a very weak solution, we prove some…
We focus in this paper on the stochastic stabilization problems of PDEs by Levy noise. Sufficient conditions under which the perturbed systems decay exponentially with a general rate function are provided and some examples are constructed…
This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
We consider the inverse problem of determining initial data in general Ornstein-Uhlenbeck equations on the Euclidean space from partial measurement localized on the so-called thick sets. Using the logarithmic convexity technique and recent…
This mini-course of 20 lectures aims at highlights of spectral theory for self-adjoint partial differential operators, with a heavy emphasis on problems with discrete spectrum. Part I: Discrete Spectrum (ODE preview, Laplacian - computable…
These notes describe some applications of the analysis of ordinary differential equations to the study of the viscous approximation of conservation laws in one space dimension. The exposition mostly focuses on the analysis of invariant…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
We study the quantitative transfer of uniqueness from the classical to the fractional Calder\'on problem with exterior data. This allows us to deduce the first stability estimates for the principal part of the isotropic fractional…
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
This paper explicitly computes the transition densities of a spectrally negative stable process with index greater than one, reflected at its infimum. First we derive the forward equation using the theory of sun-dual semigroups. The…
Necessary and sufficient stability and instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. In both cases,…
In this paper we revisit the classical Cauchy problem for Laplace's equation as well as two further related problems in the light of regularisation of this highly ill-conditioned problem by replacing integer derivatives with fractional…
An infinite irregular harmonic chain of particles is considered. We assume that some particles (``defects'') in the chain have masses and force constants of interaction different from the masses and the interaction constants of the other…
We prove the equivalence of the well-posedness of a partial differential equation with delay and an associated abstract Cauchy problem. This is used to derive sufficient conditions for well-posedness, exponential stability and norm…
We consider the Cauchy problem for semilinear parabolic equation in divergence form with obstacle. We show that under natural conditions on the right-hand side of the equation and mild conditions on the obstacle the problem has a unique…