Related papers: Stability for the Infinity-Laplace Equation with v…
Robust hyperbolicity and stability results for linear partial differential equations with delay will be given and, as an application, the effect of small delays to the asymptotic properties of feedback systems will be analyzed.
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…
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…
The work deals with establishing the solvability of a system of integro-differential equations in the situation of the double scale anomalous diffusion. Each equation of such system involves the sum of the two negative Laplace operators…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
A suitable notion of weak solution to infinite-dimensional rate-independent systems, called Inertial Balanced Viscosity (IBV) solution, is introduced. The key feature of such notion is that the energy dissipated at jump discontinuities…
We study the problem of coupling Einstein's equations to a relativistic and physically well-motivated version of the Navier-Stokes equations. Under a natural evolution condition for the vorticity, we prove existence and uniqueness in a…
In this paper we perform stability analysis for exponential solutions in Einstein-Gauss-Bonnet and cubic Lovelock gravity. We report our findings, provide areas on parameters space and discuss familiarities and differences between cases.…
A nonlinear Schr\"{o}dinger (NLS) equation with an effect of viscosity is derived from a Korteweg-de Vries (KdV) equation modified with viscosity using the method of multiple time-scales. It is well known that the plane-wave solution of the…
We consider variational principles related to V. I. Arnold's stability criteria for steady-state solutions of the two-dimensional incompressible Euler equation. Our goal is to investigate under which conditions the quadratic forms defined…
The goal of the present paper is to study the viscoelastic wave equation with the time delay \[ |u_t|^\rho u_{tt}-\Delta u-\Delta u_{tt}+\int_0^tg(t-s)\Delta u(s)ds+\mu_1u_t(x,t)+\mu_2 u_t(x,t-\tau)=b|u|^{p-2}u\] under initial boundary…
New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable…
In this paper, we are concerned with the following viscoelastic wave equation \begin{equation*} \label{1} u_{tt}-\nabla u +\int_0^t g_1 (t-s)~ div(a_1(x) \nabla u(s))~ ds + \int_0^{+ \infty} g_2 (s)~ div(a_2(x) \nabla u(t-s)) ~ds = 0,…
This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…
This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…
Jeans instability of finite massive bodies at hydrostatic equilibrium is studied. Differential equation governing the evolution of infinitesimal disturbances is derived. We take into account radial inhomogeneity of mass density and other…
We prove a stability result of constant equilibria for the three-dimensional Navier-Stokes-Poisson system uniform in the inviscid limit. We allow the initial density to be close to a constant and the potential part of the initial velocity…
The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…
We investigate the initial-value problem for the incompressible tangential Navier-Stokes equation with variable viscosity on a given two-dimensional surface without boundary. Existence of global weak and strong solutions under inhomogeneous…
We initiate the study of stability of solutions of the 2D inviscid incompressible porous medium equation (IPM). We begin by classifying all stationary solutions of the inviscid IPM under mild conditions. We then prove some linear stability…