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Blow-up of radially symmetric solutions for a semilinear heat equation on hyperbolic space

  • Ai Ling Amy PohEmail author
  • Masahiko Shimojo
Article
  • 28 Downloads

Abstract

In this paper radially symmetric solutions of a semilinear heat equation \(u_{t}=\Delta u + u^{p}\) on the hyperbolic space are considered. First universal bounds of the nonnegative solution are obtained to know the blow-up rate at the final blow-up time under the exponent p which is subcritical in the Sobolev sense. Next we derive its local blow-up profile and also analyze blow-up set of solutions.

Keywords

Semilinear parabolic equations Hyperbolic space Blow-up Universal bound Local blow-up profile Blow-up point Sobolev exponent 

Mathematics Subject Classification

35K05 35K15 35K55 35K61 

Notes

Acknowledgements

M. Shimojo was supported by JSPS KAKENHI Grant-in-Aid for Young Scientists (B) (No. 16K17634). Amy Poh Ai Ling was supported by Research Grant for Encouragement of Students, Graduate School of Natural Science and Technology, Okayama University. She is also a member of Meiji Institute for Advanced Study of Mathematical Sciences(MIMS).

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Copyright information

© Universidad Complutense de Madrid 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceOkayama UniversityOkayamaJapan
  2. 2.Department of Applied Mathematics, Faculty of ScienceOkayama University of ScienceOkayamaJapan

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