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Nonlinear Galerkin approximation of the two dimensional exterior Navier-Stokes problem
The asymptotic behavior of solutions of a semilinear parabolic equation
| 1. | Department of Mathematics, Chonnam National University, Kwangju, 500-757, South Korea, South Korea |
$u_t=\Delta u - (u^q)_y- u^p, \quad p, q >1,$
defined in the domain $Q=\{ (x, t): x=(x, y) \in \mathbf{R}^{N-1} \times \mathbf{R}, t >0 \}$ with nonnegative initial data in $L^1( \mathbf{R}^N)$. We completely classify the asymptotic profiles of solutions as $t \to \infty$ according to the parameters $p$ and $q$. We use rescaling transformations and a priori estimates.
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