Asymptotic expansion for the models of nonlinear dispersive, dissipative, equations

Details Asymptotic expansion for the models of nonlinear dispersive, dissipative, equations Asymptotic expansion for the models of nonlinear dispersive, dissipative, equations

2003-11-07

arxiv.org/abs/math/0311094v1

Mathematics

Analysis of PDEs

Scientific paper

Considered herein are the family of nonlinear equations with both dispersive and dissipative homogeneous terms appended. Solutions of these equations that start with finite energia decay to zero as time goes to infinity. We present an asymptotic form which renders explicit the influence of the dissipative, dispersive and nonlinear effect in this decay. We obtain the second term in the asymptotic expansion, as time goes to infinity of the solutions of this equations and the complete asymptotic expansion, as time goes to infinity, of the linearized equations.

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