Nonlinear Phenomena in Complex Systems, 2006, Vol.9, No.4, pp.331-351

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

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

Critical Nonlinear Dissipative Equations on a Half-Line.
Felipe Benitez and Elena I. Kaikina

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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