Instead of the L^p estimates,we study the modulation space estimates for the solution to the damped wave equation.Decay properties for both the linear and semilinear equations are obtained.The estimates in modulation ...Instead of the L^p estimates,we study the modulation space estimates for the solution to the damped wave equation.Decay properties for both the linear and semilinear equations are obtained.The estimates in modulation space differ in many aspects from those in L^p space.展开更多
The main goal of this paper is to approximate the Kuramoto-Shivashinsky(K-S for short) equation on an unbounded domain near a change of bifurcation,where a band of dominant pattern is changing stability.This leads to ...The main goal of this paper is to approximate the Kuramoto-Shivashinsky(K-S for short) equation on an unbounded domain near a change of bifurcation,where a band of dominant pattern is changing stability.This leads to a slow modulation of the dominant pattern.Here we consider PDEs with quadratic nonlinearities and derive rigorously the modulation equation,which is called the Ginzburg-Landau(G-L for short) equation,for the amplitudes of the dominating modes.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11201103 and 11471288)supported by the China Scholarship Council
文摘Instead of the L^p estimates,we study the modulation space estimates for the solution to the damped wave equation.Decay properties for both the linear and semilinear equations are obtained.The estimates in modulation space differ in many aspects from those in L^p space.
基金supported by the Deanship of Scientific Research,University of Hail,KSA(No.0150258)
文摘The main goal of this paper is to approximate the Kuramoto-Shivashinsky(K-S for short) equation on an unbounded domain near a change of bifurcation,where a band of dominant pattern is changing stability.This leads to a slow modulation of the dominant pattern.Here we consider PDEs with quadratic nonlinearities and derive rigorously the modulation equation,which is called the Ginzburg-Landau(G-L for short) equation,for the amplitudes of the dominating modes.
