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Blowing Up Solutions for Nonlinear Parabolic Systems with Unequal Elliptic Operators

  • Yohei FujishimaEmail author
  • Kazuhiro Ishige
Article
  • 29 Downloads

Abstract

We give sufficient conditions for the boundedness of the blow-up set and no boundary blow-up for type I blowing up solutions to a nonlinear parabolic system with unequal elliptic operators. We introduce a new method to simplify the nonlinear parabolic system into a scalar nonlinear parabolic inequality and investigate qualitative properties of the blow-up set.

Keywords

Nonlinear parabolic system Unequal elliptic operator Blow-up set Type-I blow-up 

Notes

Acknowledgements

The first author was supported partially by the Grant-in-Aid for Early-Career Scientists (No. 19K14569). The second author was supported partially by the Grant-in-Aid for Scientific Research (S) (No. 19H05599) from Japan Society for the Promotion of Science.

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Authors and Affiliations

  1. 1.Department of Mathematical and Systems Engineering, Faculty of EngineeringShizuoka UniversityHamamatsuJapan
  2. 2.Graduate School of Mathematical SciencesThe University of TokyoMeguro-kuJapan

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