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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (6): 787-796.doi: https://doi.org/10.1007/s10483-010-1313-6

• Articles • 上一篇    

Blow-up rate estimate for degenerate parabolic equation with nonlinear gradient term

张正策 王彪   

  1. School of Science, Xi’an Jiaotong University, Xi’an 710049, P. R. China
  • 收稿日期:2010-01-30 修回日期:2010-05-08 出版日期:2010-06-01 发布日期:2010-06-01

Blow-up rate estimate for degenerate parabolic equation with nonlinear gradient term

ZHANG Zheng-Ce, WANG Biao   

  1. School of Science, Xi’an Jiaotong University, Xi’an 710049, P. R. China
  • Received:2010-01-30 Revised:2010-05-08 Online:2010-06-01 Published:2010-06-01

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1

摘要： In this paper, the blow-up rate is obtained for a porous medium equation with a nonlinear gradient term and a nonlinear boundary flux. By using a scaling method and regularity estimates of parabolic equations, the blow-up rate determined by the interaction between the diffusion and the boundary flux is obtained. Compared with previous results, the gradient term, whose exponent does not exceed two, does not affect the blow-up rate of the solutions.

Abstract: In this paper, the blow-up rate is obtained for a porous medium equation with a nonlinear gradient term and a nonlinear boundary flux. By using a scaling method and regularity estimates of parabolic equations, the blow-up rate determined by the interaction between the diffusion and the boundary flux is obtained. Compared with previous results, the gradient term, whose exponent does not exceed two, does not affect the blow-up rate of the solutions.

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