Blow-up of Solutions to a p-Kirchhoff-Type Parabolic Equation with General Nonlinearity
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In this paper, finite time blow-up property of solutions to a p-Kirchhoff-type parabolic equation with general nonlinearity is considered. Some sufficient conditions are given for the weak solutions to blow up in finite time. An upper bound for the blow-up time is also derived. The results partially generalize some recent ones reported by Han and Li (Comput Math Appl. 2018;75:3283–3297).
Keywordsp-Kirchhoff Blowup Upper bound General nonlinearity
Mathematics Subject Classification (2010)35K20; 35K92
The author would like to express her sincere gratitude to Professor Wenjie Gao in Jilin University for his enthusiastic guidance and constant encouragement. She would also like to thank the referees for their valuable comments and suggestions which improved the original manuscript.
This study is supported by NSFC (11626044), the Natural Science Foundation of Changchun Normal University (No. 2015-002), Scientific Research Foundation for Talented Scholars of Changchun Normal University (No. RC2016-008), and Science and Technology Development Project of Jilin Province (No. 20160520103JH).
- 4.Chipot M. 2000. Elements of nonlinear analysis. Birkhauser advanced text.Google Scholar
- 6.Lions JL. On some questions in boundary value problems of mathematical physics. Contemporary developments in Continuum Mechanics and Partial Differential Equations (Proceedings of International Symposium, Inst. Mat., Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1977). North-Holland: North-Holland Mathematical Studies; 1978. p. 284–346.Google Scholar