相关论文: On multiscale Gevrey and q-Gevrey asymptotics for …

We describe the asymptotic behaviour and the stability properties of the solutions to a second order rational difference equation.

In this paper, we study the asymptotic behavior as $x_1\to+\infty$ of solutions of semilinear elliptic equations in quarter- or half-spaces, for which the value at $x_1=0$ is given. We prove the uniqueness and characterize the…

Usually when solving differential or difference equations via series solutions one encounters divergent series in which the coefficients grow like a factorial. Surprisingly, in the $q$-world the $n$th coefficient is often of the size…

In this paper we study the asymptotic behavior of solutions of fractional differential equations of the form $D^{\alpha}_Cu(t)=Au(t)+f(t)$ on the half line, where $D^{\alpha}_Cu(t)$ is the derivative of the function $u$ in Caputo's sense,…

Given a multivariate generating function F, we determine asymptotics for the coefficients. Our approach is to use Cauchy's integral formula near singular points of F, resulting in a tractable oscillating integral. This paper treats the case…

We study the asymptotic behavior of a special smooth solution y(x,t) to the second member of the Painleve I hierarchy. This solution arises in random matrix theory and in the study of Hamiltonian perturbations of hyperbolic equations. The…

Following Deift-Zhou's nonlinear steepest descent method, the long-time asymptotic behavior for the Cauchy problem of the 5th order modified Korteweg-de Vries equation is analyzed. Based on the inverse scattering transform, the 5th order…

This article deals with the asymptotic behavior of fourth order differential equation where the coefficients are perturbations of linear constant coefficient equation. We introduce a change of variable and deduce that the new variable…

In this paper, we study the algebraic relations satisfied by the solutions of $q$-difference equations and their transforms with respect to an auxiliary operator. Our main tool is the parametrized Galois theories developed in two papers.…

We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions defined, bounded and continuous on an unbounded…

In this paper, the describing of rational Riordan's arrays from the combinatorial analysis is represented as solutions of a Cauchy problem for two-dimensional difference equations and it is researched the asymptotic of these arrays.

We consider the time-dependent Navier-Stokes equations in a half-space with boundary data on the line $(x,y)=(x_0,y)$ assumed to be time-periodic (or stationary) with a fixed asymptotic velocity ${\bf u}_{\infty}=(1,0)$ at infinity. We show…

We establish analyticity of the subcritical and critical quasi-geostrophic equations in critical Besov spaces. The main method is so-called Gevrey estimates, which is motivated by the work of Foias and Temam. We show that mild solutions…

We exhibit a family of second-order hyperbolic differential operators presenting spectral transition of the Hamilton map. As a consequence we prove that the Cauchy problem is not locally solvable at the origin in Gevrey classes of order…

In this work we study the asymptotic behavior of solutions for a general linear second-order evolution differential equation in time with fractional Laplace operators in $\mathbb{R}^n$. We obtain improved decay estimates with less demand on…

In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…

The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of a previous work, where the homogeneous Erd\H os-R\'enyi…

An asymptotic small parameter expansion of a single Cauchy problem is constructed for a singularly perturbed system of hyperbolic equations describing vibrations of two rigidly connected strings. Equations (such as generalized Korteweg-de…

This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional…

We consider solutions of the Cauchy problem for semilinear equations with (possibly) different L\'evy operators. We provide various results on their convergence under the assumption that symbols of the involved operators converge to the…