Abstract
Let Mn be an embedded closed submanifold of ℝk+1 or a smooth bounded domain in ℝn, where n ≥ 3. We show that the local smooth solution to the heat flow of self-induced harmonic map will blow up at a finite time, provided that the initial map u0 is in a suitable nontrivial homotopy class with energy small enough.
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We are grateful to the referee for helpful corrections and highly constructive suggestions which substantially improved the article.
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The authors B. Chen is supported partially by NSFC (Grant Nos. 12141103 and 12301074) and Guangzhou Basic and Applied Basic Research Foundation (Grant No. 2024A04J3637)), The author Y. D. Wang is supported partially by NSFC (Grant No. 11971400) and National Key Research and Development Projects of China (Grant No. 2020YFA0712500)
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Chen, B., Wang, Y.D. Finite Time Blow-up for Heat Flows of Self-induced Harmonic Maps. Acta. Math. Sin.-English Ser. (2024). https://doi.org/10.1007/s10114-024-1623-6
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DOI: https://doi.org/10.1007/s10114-024-1623-6