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arXiv · 2201.08961

Blow-up problems for a parabolic equation coupled with superlinear source and local linear boundary dissipation

Fenglong Sun·Yutai Wang·Hongjian Yin
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Abstract

In this paper, we consider the finite time blow-up results for a parabolic equation coupled with superlinear source term and local linear boundary dissipation. Using a concavity argument, we derive the sufficient conditions for the solutions to blow up in finite time. In particular, we obtain the existence of finite time blow-up solutions with arbitrary high initial energy. We also derive the upper bound and lower bound of the blow up time.

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Fenglong Sun, Yutai Wang, Hongjian Yin. 2022-01-22. Blow-up problems for a parabolic equation coupled with superlinear source and local linear boundary dissipation. https://doi.org/10.1016/j.jmaa.2022.126327

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