相关论文: On single-frequency asymptotics for the Maxwell-Bl…

We consider non-interacting particles subject to a fixed external potential $V$ and a self-generated magnetic field $B$. The total energy includes the field energy $\beta \int B^2$ and we minimize over all particle states and magnetic…

The results of the mathematical theory of asymptotic operation developed in hep-th/9612037 are applied to problems of immediate physical interest. First, the problem of UV renormalizationis analyzed from the viewpoint of asymptotic…

The solution to Maxwell-Bloch systems using an integral-equation-based framework has proven effective at capturing collective features of laser-driven and radiation-coupled quantum dots, such as light localization and modifications of Rabi…

We study the (characteristic) Cauchy problem for the Maxwell-Bloch equations of light-matter interaction via asymptotics, under assumptions that prevent the generation of solitons. Our analysis clarifies some features of the sense in which…

We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense…

We give a complete study of the asymptotic behavior of a simple model of alignment of unit vectors, both at the level of particles , which corresponds to a system of coupled differential equations, and at the continuum level, under the form…

We simulate the transition from amplified spontaneous emission (ASE) to lasing in random systems with varying degrees of mode overlap. This is accomplished by solving the stochastic Maxwell-Bloch equations with the finite-difference…

For arbitrarily small values of $\varepsilon>0,$ we formulate and analyse the Maxwell system of equations of electromagnetism on $\varepsilon$-periodic sets $S^\varepsilon\subset{\mathbb R}^3.$ Assuming that a family of Borel measures…

Analytical stability calculation is done to prove stability properties for systems with parameters that do not have explicit values. For systems with three components, the usual method of finding the characteristic polynomial as the…

This paper is dedicated to the investigation of the asymptotic behavior of a delayed wave equation without the presence of any position term. First, it is shown that the problem is well-posed in the sense of semigroups theory. Thereafter,…

For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…

In this article we present a novel method for studying the asymptotic behaviour, with order-sharp error estimates, of the resolvents of parameter-dependent operator families. The method is applied to the study of differential equations with…

We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy…

Within the mode-coupling theory for structural relaxation in simple systems the asymptotic laws and their leading-asymptotic correction formulas are derived for the motion of a tagged particle near a glass-transition singularity. These…

The space-like asymptotic limit of the bilocal composite field of the state consisting of a nucleus and an electron is studied. It is shown that the resulting local field of an atom satisfies the proper commutation relations in the…

We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…

In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…

Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…

This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…

In this paper, we consider the Cauchy problem for a hyperbolic equation $Q(\partial_t,\partial_x)u=0$ of any order $m\geq3$, where $t\geq0$ and $x\in\mathbb{R}^n$, and $Q=P_m+P_{m-1}+P_{m-2}$ is a sum of homogeneous hyperbolic polynomials…