Scattering and modified scattering for abstract wave equations with time-dependent dissipation
نویسنده
چکیده
We consider the initial-value problem of abstract wave equations with weak dissipation. We show that under conditions on the dissipation coefficient and its derivative the solutions to the abstract dissipative equation are closely related to solutions of the free problem multiplied by a decay function. This paper gives the counterpart to a recent paper of T.Yamazaki [Adv. Differential Equ., 11(4):419–456, 2006], where effective dissipation terms and the relation to the corresponding abstract parabolic problem are considered. AMS Subject Classification: 35L90, 35L15
منابع مشابه
Simulation of Surface Plasmon Excitation in a Plasmonic Nano-Wire Using Surface Integral Equations
In this paper, scattering of a plane and monochromatic electromagnetic wave from a nano-wire is simulated using surface integral equations. First, integral equationsgoverning unknown fields on the surface is obtained based on Stratton-Cho surface integral equations. Then, the interaction of the wave with a non-plasmonic as well as a palsmonic nano-wire is considered. It is shown that in scatter...
متن کاملInvestigation of Scalar Modulation Instability in the Presence of Raman Scattering in Photonic Crystal Fibers
In this paper, by including Raman scattering in the coupled-mode equations, the scalar modulation instability in photonic crystal fibers is investigated. The evolution of the pump, Stokes and anti-Stokes waves along the fiber as well as the conversion efficiency for two cases, with and without Raman effect, are studied. The effect of anti-Stokes seed and the pump depletion on the evolution of S...
متن کاملTheoretical and Experimental Studies of Upright Perforated Wave Filters
Liu et al. (1987) proposed a theoretical solution for scattering of waves through a permeable dissipation region. On the basis of bulk dissipation of the incident wave energy, this method is extended to evaluate the reflection and transmission coefficients of waves through a wave filter composed of rows of perforated sheets aligned normally to the direction of wave propagation. The results of t...
متن کاملModified scattering for a wave equation with weak dissipation
We consider the Cauchy problem for the weakly dissipative wave equation u+ μ 1 + t ut = 0 with parameter μ ≥ 2. Based on the explicit representations of solutions provided in [Math. Meth. Appl. Sci. 2004; 27:101-124] sharp decay estimates for data from a dense subspace of the energy space are derived. Furthermore, sharpness is discussed in terms of a modified scattering theory. AMS subject clas...
متن کاملSemiclassical Singularity Propagation Property for Schrödinger Equations
Abstract We consider Schrödinger equations with variable coefficients, and it is supposed to be a long-range type perturbation of the flat Laplacian on Rn. We characterize the wave front set of solutions to Schrödinger equations in terms of the initial state. Then it is shown that the singularity propagates following the classical flow, and it is formulated in a semiclassical setting. Methods a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006