Related papers: Nonlocal dispersal equations with almost periodic …
In this paper, we focus on the nonlocal dispersal monostable equation with seasonal succession, which can be used to describe the dynamics of species in an environment alternating between bad and good seasons. We first prove the existence…
We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on…
We study a nonlinear pseudodifferential equation describing the dynamics of dislocations. The long time asymptotics of solutions is described by the self-similar profiles.
We investigate a method for extracting nonlinear principal components (NPCs). These NPCs maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate probability…
It is known that solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal equations. In…
We consider stochastic differential equations, obtained by adding weak Gaussian white noise to ordinary differential equations admitting $N$ asymptotically stable periodic orbits. We construct a discrete-time, continuous-space Markov chain,…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
The paper is concerned with asymptotic properties of the principal components analysis of functional data. The currently available results assume the existence of the fourth moment. We develop analogous results in a setting which does not…
In this paper, the asymptotics of the spectral data (eigenvalues and weight numbers) are obtained for the higher-order differential operators with distribution coefficients and separated boundary conditions. Additionally, we consider the…
We study an indefinite spectral problem for a second-order self-adjoint elliptic operator in an asymptotically thin cylinder. The operator coefficients and the spectral density function are assumed to be locally periodic in the axial…
We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a nonlocal nonlinear (cubic) term in the context of symmetry analysis using the formalism of semiclassical asymptotics. This…
We consider the operator ${d^4dt^4}+V$ on the real line with a real periodic potential $V$. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define a Lyapunov function which is analytic…
In this paper we consider a class of non-local in time telegraph equations. Recently, it has been proved that the fundamental solutions of such equations can be interpreted as the probability density function of a stochastic process. We…
We consider a stochastic partial differential equation close to bifurcation of pitchfork type, where a one-dimensional space changes its stability. For finite-time Lyapunov exponents we characterize regions depending on the distance from…
We consider a first order operator with a periodic 3x3 matrix potential on the real line. This operator appears in the problem of the periodic vector NLS equation. The spectrum of the operator covers the real line, it is union of the…
In this paper we investigate, through numerical studies, the dynamical evolutions encoded in a linear one-dimensional nonlocal equation arising in peridynamcs. The different propagation regimes ranging from the hyperbolic to the dispersive,…
Second-order characteristics including covariance and spectral density functions are fundamentally important for both statistical applications and theoretical analysis in functional time series. In the high-dimensional setting where the…
We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both…
We investigate pinning regions and unpinning asymptotics in nonlocal equations. We show that phenomena are related to but different from pinning in discrete and inhomogeneous media. We establish unpinning asymptotics using geometric…
This paper focuses on the study of semilinear fractional diffusion-wave equations in the context of critical nonlinearities. Firstly, we address the issue of local well-posedness for the problem, examine spatial regularity, and the…