On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation. (27th September 2009)

• Record Type: Journal Article
• Authors: Liang, Zongqi; Zhan, Huashui
• Other Names: Zhang Guang Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2009(2009)
• Publication Date: 2009-09-27
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2009/827087
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : By Oleinik's line method, we study the existence and the uniqueness of the classical solution of the Cauchy problem for the following equation in[ 0, T ] × R 2 :∂ x x u + u ∂ y u − ∂ t u = f ( ⋅, u ), provided thatT is suitable small. Results of numerical experiments are reported to demonstrate that the strong solutions of the above equation may blow up in finite time.