Energy partition for the linear radial wave equation
نویسندگان
چکیده
منابع مشابه
Differential Transform Method to two-dimensional non-linear wave equation
In this paper, an analytic solution is presented using differential transform method (DTM) for a class of wave equation. The emphasis is on the nonlinear two-dimensional wave equation. The procedures introduced in this paper are in recursive forms which can be used to obtain the closed form of the solutions, if they are required. The method is tested on various examples, and the results reveal ...
متن کاملThe Radial Defocusing Energy-supercritical Nonlinear Wave Equation in All Space Dimensions
We consider the defocusing nonlinear wave equation utt − Δu + |u|pu = 0 with spherically-symmetric initial data in the regime 4 d−2 < p < 4 d−3 (which is energy-supercritical) and dimensions 3 ≤ d ≤ 6; we also consider d ≥ 7, but for a smaller range of p > 4 d−2 . The principal result is that blowup (or failure to scatter) must be accompanied by blowup of the critical Sobolev norm. An equivalen...
متن کاملWeighted energy decay for 3D wave equation
We obtain a dispersive long-time decay in weighted energy norms for solutions to the 1D wave equation with generic potential. The decay extends the results obtained by Murata for the 1D Schrödinger equation.
متن کاملDevelopment of Linear Vernier Hybrid Permanent Magnet Machine for Wave Energy Converter
Today, due to the limited supply and rapid consumption of fossil fuels, transitioning towards renewable energy supplies has become more important than ever.. The purpose of this paper is to present a new linear permanent magnet vernier machine structure which is designed to capture wave energy and improve the performance of the prototype vernier machine. By halving the proposed vernier machine,...
متن کاملGlobal Well-posedness, Scattering and Blow-up for the Energy Critical Focusing Non-linear Wave Equation
In this paper we consider the energy critical non-linear wave equation ∂ t u−∆u = ± |u| 4 N−2 u (x, t) ∈ R × R u ∣∣ t=0 = u0 ∈ Ḣ1(R ) ∂tu ∣∣ t=0 = u1 ∈ L(R ) Here the − sign corresponds to the defocusing problem, while the + sign corresponds to the focusing problem. The theory of the local Cauchy problem (CP) for this equation was developed in many papers, see for instance [26], [9], [2...
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: Mathematische Annalen
سال: 2013
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-013-0970-x