Loss of regularity in the K(m, n) equations

Alon Zilburg, Philip Rosenau

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.

Original languageEnglish
Pages (from-to)2651-2665
Number of pages15
Issue number6
StatePublished - 27 Apr 2018


  • compactons
  • formation of singularity
  • waiting time


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