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Abstract
The aim of this paper is to consider the time-decay properties of the solution for the Rosenau-Burgers equation in the form In particular, we prove some algebraic time decay rates of the solution within some spatial Sobolev spaces. The asymptotic stability the solution of the corresponding of linear equation is also obtained. To prove all of these, we make using of the method of Fourier transform together with the energy method.
∗This work was partly supported by Ministry of Education of Japan Grant-in-Aid under Contract P-96196 for JSPS, and Sasakawa Scientific Research Grant N0.8-069 from the Japan Science Socity.
∗This work was partly supported by Ministry of Education of Japan Grant-in-Aid under Contract P-96196 for JSPS, and Sasakawa Scientific Research Grant N0.8-069 from the Japan Science Socity.
Notes
∗This work was partly supported by Ministry of Education of Japan Grant-in-Aid under Contract P-96196 for JSPS, and Sasakawa Scientific Research Grant N0.8-069 from the Japan Science Socity.