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

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 (...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 18; no. 6
Main Authors Ding, Hang, Zhou, Jun
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2021
Springer Nature B.V
Subjects
Epitaxial growth
Mathematical models
Mathematics
Mathematics and Statistics
Mountains
Nonlinearity
35B44
infinite time blow-up
logarithmic nonlinearity
arbitrary initial energy
35K58
35K35
Fourth-order parabolic equation
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Summary: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 ∞ ; second, we prove that the solution can blow up at ∞ 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.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-021-01880-9