This paper studies a fourth-order parabolic equation ut + ε(unuxxx)x − δ|uxx|muxx = 0 with the boundary conditions uxx = 0, u = l and the initial condition u(x, 0) = u0(x). The existence of solutions is obtained from the semidiscretization method. When the initial function is close to a constant steady state solution, the uniqueness of the bounded solutions is obtained. Finally, by the iteration technique from its semi-discrete problem, the solution exponentially converges to a constant steady state solution as the time tends to infinity.
Liang, B., Peng, X., & Shen, H. (2016). Study of Solutions to a Fourth Order Parabolic Equation∗. Mathematical Modelling and Analysis, 21(1), 1-15. https://doi.org/10.3846/13926292.2016.1127860
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