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August, 2020 A Class of Fourth-order Parabolic Equations with Logarithmic Nonlinearity
Menglan Liao, Qingwei Li
Taiwanese J. Math. 24(4): 975-1003 (August, 2020). DOI: 10.11650/tjm/190801

Abstract

In this paper, we apply the modified potential well method and the logarithmic Sobolev inequality to study the fourth-order parabolic equation with $p$-Laplacian and logarithmic nonlinearity. Some results are obtained under the different initial data conditions. More precisely, we give the global existence of weak solution by combining the classical Galerkin's method with the modified potential well method, decay estimates, and blow-up in finite time when the initial energy is subcritical and critical, respectively. In addition, sufficient conditions for the global existence and blow-up of the weak solution are also provided for supercritical initial energy. These results extend and improve many results in the literature.

Citation

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Menglan Liao. Qingwei Li. "A Class of Fourth-order Parabolic Equations with Logarithmic Nonlinearity." Taiwanese J. Math. 24 (4) 975 - 1003, August, 2020. https://doi.org/10.11650/tjm/190801

Information

Received: 4 February 2019; Revised: 17 May 2019; Accepted: 30 July 2019; Published: August, 2020
First available in Project Euclid: 13 August 2019

MathSciNet: MR4124554
Digital Object Identifier: 10.11650/tjm/190801

Subjects:
Primary: 35A01, 35B44, 35K30

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

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Vol.24 • No. 4 • August, 2020
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