Abstract
We consider the Fujita equation \(u_t={\varDelta } u+u^{p}\) on \({\mathbb {R}}^N\) with \(N\ge 3\). We prove the existence of global, unbounded solutions for \(p_S<p<p_{JL}\), where \(p_S:={(N+2)}/{(N-2)}\) and
Previously, it was known that global, unbounded solutions exist for \(p\ge p_{JL}\), whereas for \(p<p_S\) there are no such solutions.
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Acknowledgments
This research was carried out during a visit of P. Poláčik to the Tokyo Institute of Technology. P. Poláčik was upported in part by NSF Grant DMS–1161923. Eiji Yanagida was upported in part by JSPS Grant-in-Aid for Scientific Research (A) (No. 24244012).
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Poláčik, P., Yanagida, E. Global unbounded solutions of the Fujita equation in the intermediate range. Math. Ann. 360, 255–266 (2014). https://doi.org/10.1007/s00208-014-1038-2
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DOI: https://doi.org/10.1007/s00208-014-1038-2