相关论文: Averaging, Conley index continuation and recurrent…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

A continuous semiflow is introduced for linear control systems with delays in the states and controls and bounded control range. The state includes the control functions. It is proved that there exists a unique chain control set which…

In this work we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic perturbations. For the linear case, we study robustness and existence of exponential dichotomies for nonautonomous…

Rayleigh-Taylor instability (RTI) has critical importance for a broad range of processes in nature and technology, from supernovae to plasma fusion. In most instances RTI is driven by variable acceleration whereas the bulk of existing…

In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…

We study the problem of existence of orbits connecting stationary points for the nonlinear heat and strongly damped wave equations being at resonance at infinity. The main difficulty lies in the fact that the problems may have no solutions…

The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right hand sides are small. In the case that all…

Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are…

We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…

A cantilever beam under axial flow, confined or not, is known to develop self-sustained oscillations at sufficiently large flow velocities. In recent decades, the analysis of this archetypal system has been mostly pursued under linearized…

Research of delayed neural networks with variable self-inhibitions, inter-connection weights, and inputs is an important issue. %In the real world, self-inhibitions, %inter-connection weights, and inputs should vary through time. In In this…

We study a class of nonautonomous, linear, parabolic equations with unbounded coefficients on $\mathbb R^{d}$ which admit an evolution system of measures. It is shown that the solutions of these equations converge to constant functions as…

We consider a parabolic partial differential equation that can be understood as a simple model for crowds flows. Our main assumption is that the diffusivity and the source/sink term vanish at the same point; the nonhomogeneous term is…

In this Series, we study the weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion. In this part, we focus on steady solutions and develop an `adjoint method' for deriving the nonlinear amplitude…

Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or towards the set of equilibria (quasiconvergence). In this paper, we provide new formulations of…

Waves propagating through weakly disordered smooth linear media undergo a universal phenomenon called branched flow. Branched flow has been observed and studied experimentally in various systems by considering coherent waves. Recent…

A nonlinear divergence parabolic equation with dynamic boundary conditions of Wentzell type is studied. The existence and uniqueness of a strong solution is obtained as the limit of a finite difference scheme, in the time dependent case and…

We investigate the asymptotic behavior of solutions for quasilinear parabolic equations in bounded intervals. In particular, we are concerned with a special class of solutions, called interface solutions, which exhibit e metastable…

In this thesis we investigate the instabilities of superfluids at finite superflow by means of a hydrodynamical approach. We find that at a finite value of the background superfluid velocity a hydrodynamic collective mode crosses to the…

We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components which describe the coupling and the dynamics in the bulk and on the surface,…