Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 510-517.

Previous Articles     Next Articles

Blow-Up Phenomena of Solutions for a Class of Viscous Cahn-Hilliard Equation with Gradient Dependent Potentials and Sources

Qunfei Long1,*(),Jianqing Chen2   

  1. 1 School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025
    2 Department of Mathematics & FJKLMAA, Fujian Normal University, Fuzhou 350117
  • Received:2017-11-10 Online:2019-06-26 Published:2019-06-27
  • Contact: Qunfei Long
  • Supported by:
    the NSFC (Youth Fund)(11401100);the NSFC(11371091);the NSFC(11161057);the Innovation Group of 'Nonlinear Analysis and Its Applications'(IRTL1206)


In this manuscript, we study the blow-up phenomena of solutions for a class of viscous Cahn-Hilliard equation with gradient dependent potentials and source. We establish a criterion for blow-up and determine the upper bound for blow-up time by the energy method, the differential inequality and the derivative formula of the product; We determine the lower bounds for blow-up time by the differential inequality and the derivative formula of the product.

Key words: Viscous Cahn-Hilliard equation, Bounds for blow-up time, Criteria for the low-up, Differential inequality, Derivative formula of the product

CLC Number: 

  • O175