Related papers: On the output stabilizability of the diffusion equ…
In this paper, we discuss some limitations of the modified equations approach as a tool for stability analysis for a class of explicit linear schemes to scalar partial derivative equations. We show that the infinite series obtained by…
In this paper the unconditional stability of four well-known ADI schemes is analyzed in the application to time-dependent multidimensional diffusion equations with mixed derivative terms. Necessary and sufficient conditions on the parameter…
This article presents a mathematical study of the problem of identifying a time-dependent source term in transport processes described by a timefractional parabolic equation, based on noisy time-dependent measurements taken at an arbitrary…
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…
This work continues and substantially extends our recent work on switching diffusions with the switching processes that depend on the past states and that take values in a countable state space. That is, the discrete components of the…
A stabilizer based on the forwarding technique is proposed for semilinear infinite-dimensional systems in cascade form. Sufficient conditions for local exponentially stability and global asymptotic stability of the closed-loop are derived.…
It is shown that stochastic processes of diffusion type possess, in all generality, a structure of uncertainty relations and of coherent and squeezed states. This fact is used to obtain, via Nelson stochastic formulation of quantum…
We derive simplified formulas for analyzing the stability of stochastic parametrically forced linear systems. This extends the results in [T. Blass and L.A. Romero, SIAM J. Control Optim. 51(2):1099--1127, 2013] where, assuming the…
In this paper, we establish smoothness of moments of the solutions of discrete coagulation-diffusion systems. As key assumptions, we suppose that the coagulation coefficients grow at most sub-linearly and that the diffusion coefficients…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are considered under general assumptions. The existence of stationary solutions with a single internal transition layer in such reaction-diffusion systems is shown using…
Perturbations around autonomous one-dimensional single-species reaction-diffusion systems are investigated. It is shown that the parameter space corresponding to the autonomous systems is divided into two parts: In one part, the system is…
In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…
Numerical analysis is conducted for a generalized particle method for a Poisson equation. Unique solvability is derived for the discretized Poisson equation by introducing a connectivity condition for particle distributions. Moreover, by…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by a novel variational method, where the velocity profile is assumed to be monotonic and analytic. Unstable eigenvalues of the Rayleigh…
We consider a space-homogeneous gas of {\it inelastic hard spheres}, with a {\it diffusive term} representing a random background forcing (in the framework of so-called {\em constant normal restitution coefficients} $\alpha \in [0,1]$ for…
The present paper provides a sufficient condition to ensure output finite-time and fixed-time stability. Comparing with analogous researches the proposed result is less restrictive and obtained for a wider class of systems. The presented…
The stability of asymptotic profiles of solutions to the Cauchy-Dirichlet problem for Fast Diffusion Equation (FDE, for short) is discussed. The main result of the present paper is the stability of any asymptotic profiles of least energy.…
In this paper, we show for the first time the increasing stability of the inverse source problem for the n-dimensional Helmholtz equation at multiple wave numbers, which is different from the two-or three-dimensional Helmholtz equation. In…
We present a new stabilization technique for multiscale convection diffusion problems. Stabilization for these problems has been a challenging task, especially for the case with high Peclet numbers. Our method is based on a constraint…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…