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Dissipation and Decay Estimates

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania, USA, 18015-3174

    Linghai Zhang

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  1. Linghai Zhang
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Correspondence to Linghai Zhang.

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Dedicated to Professor Zhou Yulin on the occasion of his 80th birthday

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Zhang, L. Dissipation and Decay Estimates. Acta Mathematicae Applicatae Sinica, English Series 20, 59–76 (2004). https://doi.org/10.1007/s10255-004-0149-z

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  • DOI: https://doi.org/10.1007/s10255-004-0149-z

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