Related papers: Large-time asymptotics of the wave fronts length I…
In a previous work, David Vicente gave a formula showing that the wave front issued of a point of the unit disk hasa large time linear asymptotics. In the present paper, we extend the result to intgrable 2D Hamiltoniansystems.
Lying between traditional parabolic and hyperbolic equations, time-fractional wave equations of order $\alpha\in(1,2)$ in time inherit both decaying and oscillating properties. In this article, we establish a long-time asymptotic estimate…
The Cauchy problem for two dimensional difference wave operators is considered with potentials and initial data supported in a bounded region. The large time asymptotic behavior of solutions is obtained. In contrast to the continuous case…
We prove local decay estimates for the wave equation in the asymptotically Euclidean setting. In even dimensions we go beyond the optimal decay by providing the large time asymptotic profile, given by a solution of the free wave equation.…
We prove large time asymptotics for solutions of the KP I equation with small initial data. Our assumptions on the initial data rule out lump solutions but give a precise description of the radiation field at large times. Our analysis uses…
We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the…
Uniform asymptotic approximations are obtained for the prolate spheroidal wave functions, in the high-frequency case. The results are obtained by an application of certain existing asymptotic solutions of differential equations, and involve…
We consider a class of scalar quasilinear wave equations in three spatial dimensions satisfying the weak null condition. For solutions arising from small, localized, smooth data, we give an asymptotic formula describing the global…
This is the full and extended version of the brief note arXiv:1908.00938. A nontrivially solvable 4-dimensional Hamiltonian system is applied to the problem of wave fronts and to the asymptotic theory of partial differential equations. The…
The aim of this work is to expose some asymptotic series associated to some expressions involving the volume of the n-dimensional unit ball. All proofs and the methods used for improving the classical inequalities announced in the final…
Using the recent analysis of the output of the low-energy resolvent of Schr\"odinger operators on asymptotically conic manifolds (including Euclidean space) when the potential is short-range, we produce detailed asymptotic expansions for…
We study an abstract damped wave equation. We prove that the solution of the damped wave equation becomes closer to the solution of a heat type equation as time tend to infinity. As an application of our approach, we also study the…
This paper studies, in fine details, the long-time asymptotic behavior of decaying solutions of a general class of dissipative systems of nonlinear differential equations in complex Euclidean spaces. The forcing functions decay, as time…
Problems in exponential asymptotics are typically characterized by divergence of the associated asymptotic expansion in the form of a factorial divided by a power. In this paper, we demonstrate that in certain classes of problems that…
In this paper, it is proved that, in a dual context, asymptotic expansions of ordinary linear time-differential equations which possess limiting equations to their limiting equations might be obtained by first discretizing them and then…
We derive an asymptotic solution of the Einstein field equations which describes the propagation of a thin, large amplitude gravitational wave into a curved space-time. The resulting equations have the same form as the colliding plane wave…
Using distribution theory we present the moment asymptotic expansion of continuous wavelet transform in different distributional spaces for large and small values of dilation parameter $a$. We also obtain asymptotic expansions for certain…
We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck…
In this paper, we investigate the problem of blow up and sharp upper bound estimates of the lifespan for the solutions to the semilinear wave equations, posed on asymptotically Euclidean manifolds. Here the metric is assumed to be…
We study the one-dimensional Fisher-KPP equation, with an initial condition $u_0(x)$ that coincides with the step function except on a compact set. A well-known result of M. Bramson states that, as $t\to+\infty$, the solution converges to a…