Abstract
This paper deals with a reaction–diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green’s identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.
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Acknowledgements
The authors would like to thank the anonymous Referees and the Editor for valuable suggestions improving the first version of this paper. This paper is supported by NNSF of China; Shandong Provincial Natural Science Foundation, China (ZR2016AM12, ZR2017LA003); the Fundamental Research Funds for the Central Universities.
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Liu, B., Dong, M. & Li, F. Asymptotic properties of blow-up solutions in reaction–diffusion equations with nonlocal boundary flux. Z. Angew. Math. Phys. 69, 27 (2018). https://doi.org/10.1007/s00033-018-0920-2
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DOI: https://doi.org/10.1007/s00033-018-0920-2