Acta Mathematica Scientia

, Volume 39, Issue 2, pp 567–579 | Cite as

Blow-Up Phenomena for a Class of Generalized Double Dispersion Equations

  • Huafei DiEmail author
  • Yadong Shang


In this article, we study the blow-up phenomena of generalized double dispersion equations uttuxxuxxt + uxxxxuxxtt = f(ux)x. Under suitable conditions on the initial data, we first establish a blow-up result for the solutions with arbitrary high initial energy, and give some upper bounds for blow-up time T* depending on sign and size of initial energy E(0). Furthermore, a lower bound for blow-up time T* is determined by means of a differential inequality argument when blow-up occurs.

Key words

double dispersion blow up upper bound lower bound 

2010 MR Subject Classification

35L35 31A35 35B44 


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Dr. Huafei DI also specially appreciates Prof. Yue LIU for his invitation of visit to UTA.


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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceGuangzhou UniversityGuangzhouChina
  2. 2.Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education InstitutesGuangzhou UniversityGuangzhouChina

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