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Harnack estimate for a semilinear parabolic equation 被引量：1

Harnack estimate for a semilinear parabolic equation
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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 blow-up of the positive solutions and recover a classical Harnack inequality. We also obtain a result of Liouville type for the elliptic equation. 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 blow- up of the positive solutions and recover a classical Harnack inequality. We also obtain a result of Liouville type for the elliptic equation.
作者 HOU SongBo ZOU Liang
机构地区 Department of Applied Mathematics
出处 《Science China Mathematics》 SCIE CSCD 2017年第5期833-840,共8页 中国科学：数学（英文版）
关键词 parabolic equation Harnack estimate finite-time blow-up 半线性抛物方程 估计 椭圆型方程 不等式 柯西问题 有限时间 微分 正解
分类号 O175.26 [理学—基础数学] O212.1 [理学—概率论与数理统计]
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Science China Mathematics
2017年 第5期

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