An Interdisciplinary Journal

* 2006, Vol.9, No.4, pp.331-351*

In this paper we are interested in the global existence and large time behavior of solutions to the initial-boundary value problem for critical nonlinear dissipative equations

where the nonlinear term depends on the unknown function
*u* and its derivative *u _{x}* and satisfy the estimate

with such that

The linear operator is defined as follows

where the constants ,
*n*, *m* are even integers,
*m > n*. The aim of this paper is to prove the global existence of
solutions to the initial-boundary value problem (0.1). We find the main term of the asymptotic
representation of solutions.

*Key words: *
critical behavior, nonlinear dissipative equations, initial-boundary value problem

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Last updated: *January 4, 2007*