Related papers: Asymptotic Dynamical Difference between the Nonloc…
The mathematical formalism commonly used in treating nonlocal highly singular interactions is revised. The notion of support cone is introduced which replaces that of support for nonlocalizable distributions. Such support cones are proven…
A spherical cosmological model with a local void on scales of $\sim 200$ Mpc and with an inhomogeneous Hubble constant was proposed in recent two papers. This model explains consistently the observed properties of the cosmic bulk flow, the…
Axisymmetric and nonaxisymmetric patterns in the cubic-quintic Swift-Hohenberg equation posed on a disk with Neumann boundary conditions are studied via numerical continuation and bifurcation analysis. Axisymmetric localized solutions in…
The aim of this paper is to prove the existence and qualitative property of random attractors for a stochastic nonlocal delayed reaction-diffusion equation (SNDRDE) on a semi-infinite interval with a Dirichlet boundary condition on the…
In this review we discuss some results on the asymptotic dynamics of finite-dimensional open quantum systems in the Heisenberg picture. Both the spectral and algebraic approaches to this topic are addressed, with particular emphasis on…
In this paper, we have studied the long-term behavior for the projected deterministic constrained modified Swift-Hohenberg equation with constraints and Dirichlet boundary conditions. Specifically, using Lojasiewicz-Simon inequality, we…
Based on both qualitative method and numerical tests for a series of particular cases in the parameter region, a=1, 0<b <1, it is shown that the three-dimensional system (2) may have a series of interesting phenomena on the non-trivial…
In this paper, we derive optimal upper and lower bounds on the dimension of the attractor AW for scalar reaction-diffusion equations with a Wentzell (dynamic) boundary condition. We are also interested in obtaining explicit bounds about the…
In this paper, we present a nonlocal model for Poisson equation and corresponding eigenproblem with Dirichlet boundary condition. In the direct derivation of the nonlocal model, normal derivative is required which is not known for Dirichlet…
We study the dispersive properties of a linear equation in one spatial dimension which is inspired by models in peridynamics. The interplay between nonlocality and dispersion is analyzed in detail through the study of the asymptotics at low…
In this paper, we study the global dynamics of a general $2\times 2$ competition models with nonsymmetric nonlocal dispersal operators. Our results indicate that local stability implies global stability provided that one of the diffusion…
In this paper, we study two local--nonlocal settings for parabolic--elliptic evolution systems. In our problems we have a disjoint partition of the spacial domain $\Omega$ as $\Omega=A\cup B$ and we first consider a local parabolic equation…
We consider a generalized alpha-type model in the whole three-dimensional space and driven by a stationary (time-independent) external force. This model contains as particular cases some relevant equations of the fluid dynamics, among them…
We study a non-local evolution equation on the hyperbolic space $\mathbb{H}^N$. We first consider a model for particle transport governed by a non-local interaction kernel defined on the tangent bundle and invariant under the geodesic flow.…
We study asymptotic behavior of the bottom point of the spectrum of convolution type operators in environments with locally periodic microstructure. We show that its limit is described by an additive eigenvalue problem for Hamilton-Jacobi…
Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…
We study the symmetry of the class of nonlocal models which includes the nonlocal extension of the Pais-Uhlenbeck oscillator. As a consequence, we obtain an infinite dimensional symmetry algebra, containing the Virasoro algebra, which can…
We compare limit-based and scale-local dimensions of complex distributions, particularly for a strange attractor of the Henon map. Scale-local dimensions as distributions on scale are seen to exhibit a wealth of detail. Limit-based…
A new local, covariant ``counter-term'' is used to construct a variational principle for asymptotically flat spacetimes in any spacetime dimension $ d \ge 4$. The new counter-term makes direct contact with more familiar background…
It has been argued that the quantum (conformal) trace anomaly could potentially provide us with a dynamical explanation of the cosmological constant problem. In this paper, however, we show by means of a semiclassical analysis that the…