Two new blow-up conditions for a pseudo-parabolic equation with logarithmic nonlinearity

Jun Zhou; Hang Ding

doi:10.4134/BKMS.b181101

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Two new blow-up conditions for a pseudo-parabolic equation with logarithmic nonlinearity

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blow-up logarithmic nonlinearity pseudo-parabolic equation critical initial energy

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초록

This paper deals with the blow-up phenomenon of solutions to a pseudo-parabolic equation with logarithmic nonlinearity, which was studied extensively in recent years. The previous result depends on the mountain-pass level $d$ (see \eqref{d} for its definition). In this paper, we obtain two blow-up conditions which do not depend on $d$. Moreover, the upper bound of the blow-up time is obtained.

Abstract

This paper deals with the blow-up phenomenon of solutions to a pseudo-parabolic equation with logarithmic nonlinearity, which was studied extensively in recent years. The previous result depends on the mountain-pass level $d$ (see \eqref{d} for its definition). In this paper, we obtain two blow-up conditions which do not depend on $d$. Moreover, the upper bound of the blow-up time is obtained.

참고문헌 (10)

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Y. Cao, "Initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity", Electron. J. Dierential Equa-tions, 2018, pp.19~ (2018)
Hua Chen, "Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity", Journal of Differential Equations, 258(12), pp.4424~4442 (2015), Elsevier BV[DOI]
Hang Ding, "Global existence and blow-up for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity", Journal of Mathematical Analysis and Applications, 478(2), pp.393~420 (2019), Elsevier BV[DOI]
Yijun He, "Blow-up and decay for a class of pseudo-parabolic p -Laplacian equation with logarithmic nonlinearity", Computers & Mathematics with Applications, 75(2), pp.459~469 (2018), Elsevier BV[DOI]
Cong Nhan Le, "Global Solution and Blow-up for a Class of p-Laplacian Evolution Equations with Logarithmic Nonlinearity", Acta Applicandae Mathematicae, 151(1), pp.149~169 (2017), Springer Science and Business Media LLC[DOI]
Le Cong Nhan, "Global solution and blow-up for a class of pseudo p -Laplacian evolution equations with logarithmic nonlinearity", Computers & Mathematics with Applications, 73(9), pp.2076~2091 (2017), Elsevier BV[DOI]
Víctor Padrón, "Eect of aggregation on population revovery modeled by a forward-backward pseudoparabolic equation", Transactions of the American Mathematical Society, 356(07), pp.2739~2757 (2004), American Mathematical Society (AMS)[DOI]
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