A Blow-up Dichotomy for Semilinear Fractional Heat Equations
| Autor: | Laister, Robert, Sierzega, Mikolaj |
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| Rok vydání: | 2019 |
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| Zdroj: | Mathematische Annalen 381 (2021) pp. 75-90 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00208-020-02078-2 |
| Popis: | We derive a blow-up dichotomy for positive solutions of fractional semilinear heat equations on the whole space. That is, within a certain class of convex source terms, we establish a necessary and sufficient condition on the source for all positive solutions to become unbounded in finite time. Moreover, we show that this condition is equivalent to blow-up of all positive solutions of a closely-related scalar ordinary differential equation. Comment: 19 pages |
| Databáze: | arXiv |
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