Related papers: Asymptotic solutions of a nonlinear diffusive equa…
We introduce and study stochastic $N$-particle ensembles which are discretizations for general-$\beta$ log-gases of random matrix theory. The examples include random tilings, families of non-intersecting paths, $(z,w)$-measures, etc. We…
We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted…
Nonlinear reaction-diffusion systems are known to exhibit very many novel spatiotemporal patterns. Fisher equation is a prototype of diffusive equations. In this contribution we investigate the integrability properties of the generalized…
The large time behavior of nonnegative solutions to the reaction-diffusion equation $\partial_t u=-(-\Delta)^{\alpha/2}u - u^p,$ $(\alpha\in(0,2], p>1)$ posed on $\mathbb{R}^N$ and supplemented with an integrable initial condition is…
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar non-viscous diffusive dispersive conservation laws where the far field states are prescribed. We proved that the solution of the Cauchy…
We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this…
In this article, we study the long-time asymptotic properties of a non-linear and non-local equation of diffusive type which describes the rock-paper-scissors game in an interconnected population.We fully characterize the self-similar…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev--Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is given in terms of a…
A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…
In this paper, we study the asymptotic behavior of a class of nonlinear Fokker-Planck type equations in a bounded domain with periodic boundary conditions. The system is motivated by our study of grain boundary dynamics, especially under…
This paper studies large sample properties of a Bayesian approach to inference about slope parameters $\gamma$ in linear regression models with a structural break. In contrast to the conventional approach to inference about $\gamma$ that…
The asymptotic behavior of solutions to the second-order linear differential equation $d^{2}w/dz^{2}=\{u^{2}f(\alpha,z)+g(z)\}w$ is analyzed for a large real parameter $u$ and $\alpha\in[0,\alpha_{0}]$, where $\alpha_{0}>0$ is fixed. The…
A subdiffusion problem in which the diffusion term is related to a stable stochastic process is introduced. Linear models of these systems have been studied in a general way, but non-linear models require a more specific analysis. The model…
The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…
In the present study, we find that the surface quasi-geostrophic equation admits exact solutions, which evolve with time in quasi-stationary states. The solutions presented are available for any dissipation effect $\kappa (-\Delta)^\alpha$…
This contribution presents an asymptotic formulation for the stick-slip behaviour of incomplete contacts under oscillatory variation of normal load, moment, shear load and differential bulk tension. The asymptotic description allows us not…
An $N$-dimensional nonlinear Fokker-Planck equation is investigated here by considering the time dependence of the coefficients, where drift-controlled and source terms are present. We exhibit the exact solution based on the generalized…
The stability of $q$-Gaussian distributions as particular solutions of the linear diffusion equation and its generalized nonlinear form, $\pderiv{P(x,t)}{t} = D \pderiv{^2 [P(x,t)]^{2-q}}{x^2}$, the \emph{porous-medium equation}, is…