Blow-up and global solutions for quasilinear parabolic equations with Neumann boundary conditions |
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| Authors: | Xuyan Gao Bao-Zhu Guo |
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| Affiliation: | 1. School of mathematical Sciences , Shanxi University , Taiyuan 030006, P.R. China;2. Academy of Mathematics and Systems Science, Academia Sinica , Beijing 100190, P.R. China;3. School of computational and Applied Mathematics , University of the Witwatersrand , Wits 2050, Johannesburg, South Africa |
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| Abstract: | Using the upper and lower solution techniques and Hopf's maximum principle, the sufficient conditions for the existence of blow-up positive solution and global positive solution are obtained for a class of quasilinear parabolic equations subject to Neumann boundary conditions. An upper bound for the ‘blow-up time’, an upper estimate of the ‘blow-up rate’, and an upper estimate of the global solution are also specified. |
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| Keywords: | quasilinear parabolic equation blow-up solution global solution Neumann boundary conditions blow-up time |
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