Harnack estimate for a semilinear parabolic 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 resu...
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Published in | Science China. Mathematics Vol. 60; no. 5; pp. 833 - 840 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Beijing
Science China Press
01.05.2017
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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Bibliography: | 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. 11-5837/O1 parabolic equation, Harnack estimate, finite-time blow-up |
ISSN: | 1674-7283 1869-1862 |
DOI: | 10.1007/s11425-016-0270-6 |