Wave Equation with Slowly Decaying Potential: asymptotics of Solution and Wave Operators
نویسندگان
چکیده
منابع مشابه
Wave Equation with Slowly Decaying Potential: Asymptotics of Solution and Wave Operators
In this paper, we will study the long-time behavior of y(x, t) which is the main question of the scattering theory for (1). The scattering theory of wave equation is the classical subject and was extensively studied in the literature (see [9] for an excellent source of information). It is known that the spectrum of stationary operator can be pure point as long as q ∈ L(R) with p > 2 [10, 12] an...
متن کاملScattering and Wave Operators for One-dimensional Schrödinger Operators with Slowly Decaying Nonsmooth Potentials
Let us discuss the case where the operator is defined on a half-axis, with some selfadjoint boundary condition at zero. We are interested in potentials decaying at infinity, for which we may expect that asymptotically as time tends to infinity, motion of the associated perturbed quantum system resembles the free evolution. What is the critical rate of decay of the potential for which the dynami...
متن کاملNumerical solution of the wave equation using shearlet frames
In this paper, using shearlet frames, we present a numerical method for solving the wave equation. We define a new shearlet system and by the Plancherel theorem, we calculate the shearlet coefficients.
متن کاملNUMERICAL SOLUTION OF ONE-DIMENSIONAL HEAT AND WAVE EQUATION BY NON-POLYNOMIAL QUINTIC SPLINE
This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...
متن کاملMoment bounds and asymptotics for the stochastic wave equation
We consider the stochastic wave equation on the real line driven by space–time white noise and with irregular initial data. We give bounds on higher moments and, for the hyperbolic Anderson model, explicit formulas for second moments. These bounds imply weak intermittency and allow us to obtain sharp bounds on growth indices for certain classes of initial conditions with unbounded support. c ⃝ ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Modelling of Natural Phenomena
سال: 2010
ISSN: 0973-5348,1760-6101
DOI: 10.1051/mmnp/20105405