Publications [#244244] of Thomas P. Witelski

Papers Published

1. Hwang, HJ; Witelski, TP, Short-time pattern formation in thin film equations, Discrete and Continuous Dynamical Systems, vol. 23 no. 3 (March, 2009), pp. 867-885, American Institute of Mathematical Sciences (AIMS), ISSN 1078-0947 (doi: 10.3934/dcds.2009.23.867.) [displayArticles.jsp], [doi]
   (last updated on 2024/04/18)

   Abstract:
   We study the early stages of the nonlinear dynamics of pattern formation for unstable generalized thin film equations. For unstable constant steady states, we obtain rigorous estimates for the short- to intermediate-time nonlinear evolution which extends the mathematical characterization for pattern formation derived from linear analysis: formation of patterns can be bounded by the finitely many dominant growing eigenmodes from the initial perturbation.