Abstract
In this paper, we consider the blow-up problem of the following porous medium equations with nonlinear boundary conditions
where \(m>1\), \(\Omega \subset \mathbb {R}^{n} \ (n\ge 2)\) is a bounded convex domain with smooth boundary. Under appropriate assumptions on the data, a criterion is given to guarantee that solution u blows up at finite time, and an upper bound for blow-up time is derived. Moreover, a lower bound for blow-up time is also obtained.
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This work was supported by the National Natural Science Foundation of China (No. 61473180).
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Ding, J., Shen, X. Blow-up time estimates in porous medium equations with nonlinear boundary conditions. Z. Angew. Math. Phys. 69, 99 (2018). https://doi.org/10.1007/s00033-018-0993-y
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DOI: https://doi.org/10.1007/s00033-018-0993-y