Harnack estimate for a semilinear parabolic equation

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（5）
• 页码范围: 833-840
• 页数: 8页
• 语种: 英文
• DOI: 10.1007/s11425-016-0270-6

摘要

We study the Cauchy problem of a semilinear parabolic equation.We construct an appropriate Harnack quantity and get a differential Harnack inequality.Using this inequality,we prove the finite-time blowup of the positive solutions and recover a classical Harnack inequality.We also obtain a result of Liouville type for the elliptic equation.