Global existence,nonexistence and asymptotic behavior of solutions for the Cauchy problem of semilinear heat equations |
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Authors: | Yacheng Liu Runzhang XuTao Yu |
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Affiliation: | College of Science, Harbin Engineering University, Harbin 150001, People’s Republic of China |
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Abstract: | In this paper, we study the Cauchy problem of semilinear heat equations. By introducing a family of potential wells, we first prove the invariance of some sets and isolating solutions. Then we obtain a threshold result for the global existence and nonexistence of solutions. Finally we discuss the asymptotic behavior of the solution. |
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Keywords: | 35K30 35G25 |
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