期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2004
卷号：2004
DOI：10.1155/S0161171204303133
出版社：Hindawi Publishing Corporation
摘要：We study large-time asymptotic behavior of solutions to the Cauchy
problem for a model of nonlinear dissipative evolution equation. The linear part is a pseudodifferential operator and the nonlinearity is a cubic pseudodifferential operator defined by means of the inverse Fourier transformation and represented by
bilinear and trilinear forms with respect to the direct Fourier transform of the dependent variable. We consider nonconvective type nonlinearity, that is, we suppose that the total mass of the nonlinear term does not vanish. We consider the initial data,
which have a nonzero total mass and belong to the weighted Sobolev space with a sufficiently small norm. Then we give the main term of the large-time asymptotics of solutions in the critical case. The time decay rate have an additional logarithmic
correction in comparison with the corresponding linear case.
