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山东大学学报(理学版) ›› 2018, Vol. 53 ›› Issue (8): 77-83.doi: 10.6040/j.issn.1671-9352.0.2017.341

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带有梯度超线性项抛物方程黏性解的比较原理

王俊芳,赵培浩   

  1. 兰州大学数学与统计学院, 甘肃 兰州 730000
  • 收稿日期:2017-06-30 出版日期:2018-08-20 发布日期:2018-07-11
  • 作者简介:王俊芳(1982— ),女,博士,讲师,研究方向为完全非线性方程的黏性解的存在及边界爆破. E-mail:wangjunfang0309@126.com
  • 基金资助:
    国家自然科学基金资助项目(11471147)

Comparison principles for viscosity solution of fully nonlinear parabolic equations with superlinear gradient nonlinearities

WANG Jun-fang, ZHAO Pei-hao   

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu, China
  • Received:2017-06-30 Online:2018-08-20 Published:2018-07-11

摘要: 研究梯度具有超线性增长的完全非线性抛物方程问题,证明了具有超线性增长的半连续黏性上下解的比较原理的存在,并且把此结果延伸到单调抛物系统中。

关键词: 退化抛物方程, 超线性增长, 黏性解, 单调系统, 比较原理

Abstract: A problem of fully nonlinear degenerate parabolic partial differential equations with a superlinear gradient nonlinearity is studied. A comparison result is proved between semicontinuous viscosity subsolutions and supersolutions having superlinear growth. We extend our result to monotone systems of parabolic equations.

Key words: degenerate parabolic equations, viscosity solution, comparison principle, monotone system, superlinear growth

中图分类号: 

  • O177
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