Related papers: A note on stability shifting for the Muskat proble…
We consider a transmission problem where a structurally damped plate equation is coupled with a damped or undamped wave equation by transmission conditions. We show that exponential stability holds in the damped-damped situation and…
Oscillating solutions to the effective equations of Loop Quantum Cosmology have been suggested for the role of an `eternal seed', providing a possible starting point for the emergent universe scenario. We investigate the stability of a…
In this paper we propose new sufficient conditions for stability of solutions of systems of Volterra linear integral equations and systems of linear integro-differential Volterra equations. Solution stability conditions for systems of…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
We study the dynamics of small fluctuations about the uniform state of a crystal moving through a dissipative medium, e.g. a sedimenting colloidal crystal or a moving flux lattice, using a set of continuum equations for the displacement…
Results on the problem of stabilizing a nonlinear continuous-time system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive…
Bouncing solutions are obtained from a generally covariant action characterized by a potential which is a nonlocal functional of the dilaton field at two separated space-time points. Gradient instabilities are shown to arise in this context…
Multistability cannot be derived from any theoretical model that is based on a monostable master equation. On the other hand, multistability is experimentally-observed in a variety of quantum systems. A master equation having a nonlinear…
We investigate the two-dimensional Muskat problem with a nonlinear elastic interface, for both one-phase and two-phase scenarios. Following the framework developed by Nguyen [35,36], we demonstrate that the problem is locally well-posed in…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
The paper deals with the extremum seeking problem for a class of cost functions depending only on a part of state variables of a control system. This problem is related to the concept of partial asymptotic stability and analyzed by…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
We first prove local-in-time well-posedness for the Muskat problem, modeling fluid flow in a two-dimensional inhomogeneous porous media. The permeability of the porous medium is described by a step function, with a jump discontinuity across…
In this study, we address the inverse problem of recovering the Lam\'e parameters ($\lambda, \mu$) and the density $\rho$ of a medium from the Neumann-to-Dirichlet map for any dimension $d\geq 2$. This inverse problem finds its motivation…
This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…
The profiles of narrow lattice solitons are calculated analytically using perturbation analysis. A stability analysis shows that solitons centered at a lattice (potential) maximum are unstable, as they drift toward the nearest lattice…
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large…
We introduce a large family of homogeneous and isotropic cosmological solutions in quadratic gravity which are singularity-free at early and late times. This kind of smooth solutions only emerges beyond the unstable de Sitter branch…