BLOW-UP PHENOMENA FOR A CLASS OF GENERALIZED DOUBLE DISPERSION EQUATIONS

doi:10.1007/s10473-019-0219-1

Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (2): 567-579.doi: 10.1007/s10473-019-0219-1

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BLOW-UP PHENOMENA FOR A CLASS OF GENERALIZED DOUBLE DISPERSION EQUATIONS

Huafei DI, Yadong SHANG

School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China

Received:2017-11-19 Revised:2018-04-09 Online:2019-04-25 Published:2019-05-06
Contact: Huafei DI E-mail:dihuafei@yeah.net
Supported by:
This research is partially supported by the NSF of China (11801108, 11626070), the Scientific Program of Guangdong Province (2016A030310262), and the College Scientific Research Project of Guangzhou City (1201630180).

Abstract

Abstract: In this article, we study the blow-up phenomena of generalized double dispersion equations u_tt - u_xx - u_xxt + u_xxxx - u_xxtt = f(u_x)_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

Huafei DI, Yadong SHANG. BLOW-UP PHENOMENA FOR A CLASS OF GENERALIZED DOUBLE DISPERSION EQUATIONS[J].Acta mathematica scientia,Series B, 2019, 39(2): 567-579.

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BLOW-UP PHENOMENA FOR A CLASS OF GENERALIZED DOUBLE DISPERSION EQUATIONS

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