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 ux 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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