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Dissipation and Decay Estimates

Dissipation and Decay Estimates
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摘要 We establish the optimal rates of decay estimates of global solutions of some abstract differential equations, which include many partial differential equations. We provide a general treatment so that any future problem will enjoy the decay estimates displayed here as long as the general hypotheses are satisfied. The main hypotheses are the existence of global solutions of the equations and some growth control of the Fourier transform of the solutions. We establish the optimal rates of decay of the solutions for initial data in different spaces. The main ingredients and technical tools are the Fourier splitting method, the iteration skill and the energy estimates.
作者 LinghaiZhang
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2004年第1期59-76,共18页 应用数学学报(英文版)
关键词 Partial differential equations global solutions decay estimates Fourier splitting technique Partial differential equations global solutions decay estimates Fourier splitting technique
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