Related papers: Stability of nonlinear dissipative systems with ap…
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 study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
Anomalous dissipation is a dissipation mechanism of kinetic energy which is established by a sufficiently spatially rough velocity field. It implies that the rescaled mean kinetic energy dissipation rate becomes constant with respect to…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type II…
We consider the fractional unforced Burgers equation in the one-dimensional space-periodic setting: $$\partial u/\partial t+(f(u))_x +\nu \Lambda^{\alpha} u= 0, t \geq 0,\ \mathbb{x} \in \mathbb{T}^d=(\mathbb{R}/\mathbb{Z})^d.$$ Here $f$ is…
The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous…
In this work we want to explore the relationship between certain eigenvalue condition for the symbols of first order partial differential operators describing evolution processes and the linear and nonlinear stability of their stationary…
A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation of the plate is introduced: well-posedness and existence of…
In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
In this paper, we study the backward problem of determining initial condition for some class of nonlinear parabolic equations in multidimensional domain where data are given under random noise. This problem is ill-posed, i.e., the solution…
Several fluid systems are characterised by time reversal and parity breaking. Examples of such phenomena arise both in quantum and classical hydrodynamics. In these situations, the viscosity tensor, often dubbed ``odd viscosity'', becomes…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
Scaling in the dynamical properties of complex many-body systems has been of strong interest since turbulence phenomena became the subject of systematic mathematical studies. In this article, dynamical critical phenomena far from…
A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…
We present results for the 1 dimensional stochastically forced Burgers equation when the spatial range of the forcing varies. As the range of forcing moves from small scales to large scales, the system goes from a chaotic, structureless…
This paper is concerned with stability analysis and synthesis for discrete-time linear systems with stochastic dynamics. Equivalence is first proved for three stability notions under some key assumptions on the randomness behind the…
Fractional Burgers equations pose substantial challenges for classical numerical methods due to the combined effects of nonlocality and shock-forming nonlinear dynamics. In particular, linear approximation frameworks-such as spectral,…
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…