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Infinite Time Blow-Up of Solutions to a Fourth-Order Nonlinear Parabolic Equation with Logarithmic Nonlinearity Modeling Epitaxial Growth

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Abstract

This paper deals with a fourth-order nonlinear parabolic equation with logarithmic nonlinearity coming from the modeling of epitaxial growth. First, by establishing a new infinite time blow-up condition which is independent of the mountain-pass level, we show the solution can be extended over time (the whole half line) and then blows up at \(\infty \); second, we prove that the solution can blow up at \(\infty \) with arbitrary initial energy using this new infinite time blow-up condition; thirdly, some numerical simulations are presented to verify and illustrate the theoretical results. The results of this paper complete and extend the previous studies on this type of model.

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  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Hang Ding & Jun Zhou

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  1. Hang Ding
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  2. Jun Zhou
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Correspondence to Jun Zhou.

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Ding, H., Zhou, J. Infinite Time Blow-Up of Solutions to a Fourth-Order Nonlinear Parabolic Equation with Logarithmic Nonlinearity Modeling Epitaxial Growth. Mediterr. J. Math. 18, 240 (2021). https://doi.org/10.1007/s00009-021-01880-9

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  • DOI: https://doi.org/10.1007/s00009-021-01880-9

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