Global Existence and Blow-Up for the Pseudo-parabolic p(x)-Laplacian Equation with Logarithmic Nonlinearity

Zeng, Fugeng; Deng, Qigang; Wang, Dongxiu

doi:10.1007/s44198-021-00010-z

Cited by 7 publications

(2 citation statements)

References 22 publications

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“…Later, many authors [26], [27], [23] considered pseudo-parabolic equations with logarithmic nonlinearity and established results for local and global existence, uniqueness, decay estimate and asymptotic behaviour of solutions, blow-up results. Logarithmic nonlinearities in parabolic and pseudoparabolic equations were studied by Lakshmipriya et.al [11], [10] and other researchers [29], [9], [5] and they proved the existence of weak solutions and their blow up in finite time. Lower bound of Blow-up time to a fourth order parabolic equation modelling epitaxial thin film growth Recently, higher-order equations have gained much importance in studies.…”

Section: Introductionmentioning

confidence: 99%

p-Biharmonic Pseudo-Parabolic Equation with Logarithmic Non linearity

Jayachandran¹,

Gnanavel²

2022

3C TIC

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Section: Introductionmentioning

confidence: 99%

p-Biharmonic Pseudo-Parabolic Equation with Logarithmic Non linearity

Jayachandran¹,

Gnanavel²

2022

3C TIC

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“…The weak solutions of Equation (11) were obtained under suitable conditions. Moreover, Zeng et al in [33] were devoted to the study of equations with logarithmic nonlinearity and variable exponents by applying the logarithmic inequality.…”

Section: Introductionmentioning

confidence: 99%

(p(x),q(x))-Kirchhoff-Type Problems Involving Logarithmic Nonlinearity with Variable Exponent and Convection Term

Qian

et al. 2022

Fractal Fract

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In the present article, we study a class of Kirchhoff-type equations driven by the (p(x), q(x))-Laplacian. Due to the lack of a variational structure, ellipticity, and monotonicity, the well-known variational methods are not applicable. With the help of the Galerkin method and Brezis theorem, we obtain the existence of finite-dimensional approximate solutions and weak solutions. One of the main difficulties and innovations of the present article is that we consider competing (p(x), q(x))-Laplacian, convective terms, and logarithmic nonlinearity with variable exponents, another one is the weaker assumptions on nonlocal term Mv(x) and nonlinear term g.

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A pseudo‐parabolic equation with logarithmic nonlinearity: Global existence and blowup of solutions

Jayachandran,

Soundararajan

2024

Math Methods in App Sciences

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This article deals with a fourth‐order pseudo‐parabolic partial differential equation with logarithmic nonlinearity. We adopt the Faedo–Galerkin method to analyze the global existence of weak solutions and discuss the existence of a solution in subcritical and critical initial energy situations. Further, applying the concavity approach, we have shown that the solution blows up when the initial energy is subcritical, critical, and supercritical. Moreover, we have provided an upper and lower bound for blow‐up time and a decay estimate for the global solutions.

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Global Existence and Blow-Up for the Pseudo-parabolic p(x)-Laplacian Equation with Logarithmic Nonlinearity

Cited by 7 publications

References 22 publications

p-Biharmonic Pseudo-Parabolic Equation with Logarithmic Non linearity

p-Biharmonic Pseudo-Parabolic Equation with Logarithmic Non linearity

(p(x),q(x))-Kirchhoff-Type Problems Involving Logarithmic Nonlinearity with Variable Exponent and Convection Term

A pseudo‐parabolic equation with logarithmic nonlinearity: Global existence and blowup of solutions

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