Abstract
This paper is devoted to studying a fourth-order parabolic equation u t + ε ( u n u x x x ) x − δ u x x = 0 with Dirichlet boundary. By transforming the fourth order problem into an elliptic-parabolic system and applying a semidiscretization method, the existence, uniqueness and regularization of solutions are obtained. By introducing an energy functional through the semi-discrete problem, we use the iteration method to show that the solutions of the developing equation exponentially converge to a constant steady state solution as the time variable t → ∞ . Finally, we get the result of the asymptotic limit δ → 0 .
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