相关论文: Asymptotics of scalar waves on long-range asymptot…
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…
We examine the large-time behavior of axisymmetric solutions without swirl of the Navier--Stokes equation in $\mathbb{R}^3$. We construct higher-order asymptotic expansions for the corresponding vorticity. The appeal of this work lies in…
We consider the Cauchy problem for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions. Under the null condition for such systems, the global existence of small amplitude solutions is known. In…
The asymptotic symmetry analysis of Maxwell theory at spatial infinity of Minkowski space with $d\geq 3$ is performed. We revisit the action principle in de Sitter slicing and make it well-defined by an asymptotic gauge fixing. In…
We discuss the asymptotic symmetry algebra of the Schrodinger-invariant metrics in d+3 dimensions and its realization on finite temperature solutions of gravity coupled to matter fields. These solutions have been proposed as gravity…
We consider the asymptotic behavior of the soltion to the wave equation with time-dependent damping and analytic nonlinearity. Our main goal is to prove the convergence of a global solution to an equilibrium as time goes to infinity by…
We prove the global asymptotic stability of the Minkowski space for the massless Einstein-Vlasov system in wave coordinates. In contrast with previous work on the subject, no compact support assumptions on the initial data of the Vlasov…
We show that Toda shock waves are asymptotically close to a modulated finite gap solution in the region separating the soliton and the elliptic wave regions. We previously derived formulas for the leading terms of the asymptotic expansion…
We study the Cauchy problem for a nonlinear damped wave equation. Under suitable assumptions for the nonlinearity and the initial data, we obtain the global solution which satisfies weighted $L^1$ and $L^\infty$ estimates. Furthermore, we…
We apply the results of arXiv:1301.5633 to describe asymptotic behavior of linear waves on stationary Lorentzian metrics with r-normally hyperbolic trapped sets, in particular Kerr and Kerr-de Sitter metrics with |a|<M and M\Lambda a << 1.…
We consider singularly perturbed second order elliptic system in the whole space with fast oscillating coefficients. We construct the complete asymptotic expansions for the eigenvalues converging to the isolated ones of the homogenized…
We review the proof of existence and uniqueness of solutions of the Maxwell-Schr"odinger system in a neighborhood of infinity in time, with prescribed asymptotic behaviour defined in terms of asymptotic data, without any restriction on the…
This paper proves the asymptotic stability of the multidimensional wave equation posed on a bounded open Lipschitz set, coupled with various classes of positive-real impedance boundary conditions, chosen for their physical relevance:…
Uniform asymptotic expansions involving exponential and Airy functions are obtained for Laguerre polynomials $L_{n}^{(\alpha)}(x)$, as well as complementary confluent hypergeometric functions. The expansions are valid for $n$ large and…
We give a short proof of asymptotic completeness and global existence for the cubic Nonlinear Klein-Gordon equation in one dimension. Our approach to dealing with the long range behavior of the asymptotic solution is by reducing it, in…
We study a family of nonlinear damped wave equations indexed by a parameter $\epsilon >0$ and forced by a space-time white noise on the two dimensional torus, with polynomial and sine nonlinearities. We show that as $\epsilon \to 0$, the…
We consider the Riemannian random wave model of Gaussian linear combinations of Laplace eigenfunctions on a general compact Riemannian manifold. With probability one with respect to the Gaussian coefficients, we establish that, both for…
We develop a time-domain numerical framework for global scalar wave scattering in Minkowski spacetime. The main contribution is an exact conformal matching of three compactified regions: a past hyperboloidal domain attached to $\mathscr…
We investigate the asymptotic structure of electromagnetism in Minkowski space in even and odd spacetime dimensions $\geq 4$. We focus on $d>4$ since the case $d=4$ has been studied previously at length. We first consider spatial infinity…
We study the full asymptotic expansion of the monodromy data ({\it i.e.}, Stokes multipliers) for the first Painlev\'{e} transcendent (PI) with large initial data or large pole parameters. Our primary approach involves refining the complex…