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For nonlinear wave equations with a potential term we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method…
We consider the decay problem for global solutions of the Skyrme and Adkins-Nappi equations. We prove that the energy associated to any bounded energy solution of the Skyrme (or Adkins-Nappi) equation decays to zero outside the light cone…
We consider an approach to the Hawking effect which is free of the asymptotic behavior of the metric or matter fields, and which is not confined to one specific metric configuration. As a result, we find that for a wide class of spacetime…
We derive expressions for the energy, linear momentum, and angular momentum content of circularly polarized Laguerre-Gaussian wave-packets propagating in free space. The vectorial nature of the electromagnetic field is taken into account,…
We study the global existence and decay estimates for nonlinear wave equations with the space-time dependent dissipative term in an exterior domain. The linear dissipative effect may vanish in a compact space region. Moreover the nonlinear…
We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates, uniformly with respect to the space and/or time…
It can be agreed that the linear superposition and energy conservation are two independent physics laws in general. The former allows the energy to be re-distributed over space and the latter restricts the energy in the total amount.…
Total vacuum energy of some quantized fields in conical space with additional boundary conditions is calculated. These conditions are imposed on a cylindrical surface which is coaxial with the symmetry axis of conical space. The explicit…
In this paper, a class of variable-coefficient wave equations equipped with time-dependent damping and the nonlinear source is considered. We show that the total energy of the system decays to zero with an explicit and precise decay rate…
We determine the energy loss spectrum per time-interval of a relativistic charge traversing a dispersive medium. Polarization and absorption effects in the medium are modelled via a complex index of refraction. We find that the spectrum…
We give asymptotics for Einstein vacuum equations in wave coordinates with small asymptotically flat data. We show that the behavior is wave like at null infinity and homogeneous towards time like infinity. We use the asymptotics to show…
It is known that relativistic wavefunctions formally propagate beyond the light cone when the propagator is limited to the positive energy sector. By construction, this is the case for solutions of the Salpeter (or relativistic…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
In a recent paper [J. Math. Phys. 47 082303 (2006)], Quantum Energy Inequalities were used to place simple geometrical bounds on the energy densities of quantum fields in Minkowskian spacetime regions. Here, we refine this analysis for…
In this work, based on the worldline path integral representation of the vacuum energy in spacetime with a Lorentzian metric, we provide a new but complementary interpretation of the Unruh effect. We perform the quantization of the massless…
We extend the results of our paper "Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0" written with Laure Saint-Raymond to the case of forced linear wave equations in any dimension. We prove that, in dimension…
We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic…
In this paper we discuss energy conservation issues related to the numerical solution of the nonlinear wave equation. As is well known, this problem can be cast as a Hamiltonian system that may be autonomous or not, depending on the…
This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems on the…
We study compact polyhedral surfaces as Riemann surfaces and their discrete counterparts obtained through quadrilateral cellular decompositions and a linear discretization of the Cauchy-Riemann equation. By ensuring uniformly bounded…