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For the numerical simulation of time-dependent problems, recent works suggest the use of a time marching scheme based on a tensorial decomposition of the time axis. This time-separated representation is straightforwardly introduced in the…
This paper is concerned with space-time homogenization problems for damped wave equations with spatially periodic oscillating elliptic coefficients and temporally (arithmetic) quasi-periodic oscillating viscosity coefficients. Main results…
We establish the existence of spatially localised one-dimensional free surfaces of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetisation law. It is shown that the ferrohydrostatic equations can…
We study forced oscillations on differentiable manifolds which are globally defined as the zero set of appropriate smooth maps in some Euclidean spaces. Given a T-periodic perturbative forcing field, we consider the two different scenarios…
We consider hyperbolic equations with time-dependent coefficients and develop an abstract framework to derive the asymptotic behaviour of the representation of solutions for large times. We are dealing with generic situations where the…
A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g., clear mobility edges [Y. Wang et al., Phys. Rev. Lett. \textbf{125}, 196604 (2020)]. We generalize this…
In this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracking domains.
We investigate the ergodicity of 2D large scale quasigeostrophic flows under random wind forcing. We show that the quasigeostrophic flows are ergodic under suitable conditions on the random forcing and on the fluid domain, and under no…
We establish new sufficient conditions for the existence of classical hyperbolic quasiperiodic solutions for natural Lagrangian system on Riemannian manifold with time-quasiperiodic force function
In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of classical hamiltonian systems that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure plays a…
In many occurrences of fluid-structure interaction time-periodic motions are observed. We consider the interaction between a fluid driven by the three dimensional Navier-Stokes equation and a two dimensional linearized elastic Koiter shell…
In this article, we prove global existence of classical solutions to the incompressible isotropic Hookean elastodynamics in three-dimensional thin domain $\Omega_\delta=\mathbb{R}^2\times [0,\delta]$ with periodic boundary condition.
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…
Parasupersymmetry of the one dimensional time-dependent Schr\"odinger equation is established. It is intimately connected with a chain of the time-dependent Darboux transformations. As an example a parasupersymmetric model of…
We study the isotropic XY quantum spin chain with a time-periodic transverse magnetic field acting on a single site. The asymptotic problem can be mapped into a highly resonant Floquet-Schr\"odinger equation, for which, under a…
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
Spherically symmetric time-dependent solutions for the 5D system of a scalar field canonically coupled to gravity are obtained and identified as an extension of recent results obtained by Ahmed, Grzadkowskia and Wudkab. The corresponding…
In this paper we investigate the properties of the set of T-periodic solutions of semi-explicit parametrized Differential-Algebraic Equations with non-autonomous constraints of a particular type. We provide simple, degree theoretic…
We model the dynamical behavior of a three dimensional (3-D) dissipative oscillator consisting of a $m$-block whose vertical fall occurs against a spring and which can also slide horizontally on a rigid truss rotating at a known angular…
The generalized Swift--Hohenberg equation with a quadratic-cubic nonlinearity is used to study the persistence and decay of localized patterns in the presence of time-periodic parametric forcing. A novel resonance phenomenon between the…