Loss of regularity in the K(m, n) equations. (27th April 2018)

• Record Type: Journal Article
• Authors: Zilburg, Alon; Rosenau, Philip
• Is Part Of: Nonlinearity. Volume 31:Number 6(2018:Jun.)
• Page Start: 2651
• Page End: 2665
• Publication Date: 2018-04-27
• Subjects: compactons -- formation of singularity -- waiting time; 35Q53; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aab58b
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: Using a priori estimates we prove that initially nonnegative, smooth and compactly supported solutions of the equations must lose their smoothness within a finite time. Formation of a singularity is a prerequisite for the subsequent emergence of compactons. Numerical studies are presented that demonstrate two manifestations of the emerging singularity: either propagation of the right front downstream or the formation of an oscillatory tail upstream. Formation of one type of motion does not preclude the possible formation of the other at a later time.