Global solution and blow-up for a class of pseudo <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>p</mml:mi></mml:math>-Laplacian evolution equations with logarithmic nonlinearity

Nhan, Le Cong; Trường, Lê Xuân

doi:10.1016/j.camwa.2017.02.030

Cited by 75 publications

(21 citation statements)

References 20 publications

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“…Next, by (A3), Gagliardo-Nirenberg interpolation inequality (see Nhan and Truong 16 and He te al 17 ) and Young inequality, we obtain…”

Section: Local Existence and Global Existencementioning

confidence: 87%

“…Firstly, we construct an approximate weak solution of the problem via Galerkin method (see other works()). In the space

W_{0}^{1, p} false(normalΩ false),

we take an orthogonal basis

{false{ω_{j} false}}_{j = 1}^{\infty}

.…”

Section: Local Existence and Global Existencementioning

confidence: 99%

“…In this section, we establish the existence of local and global weak solutions for problem (1.1). Firstly, we construct an approximate weak solution of the problem (1.1) via Galerkin method (see other works [16][17][18][19] ). In the space W 1,p 0 (Ω), we take an orthogonal basis { } ∞ =1 .…”

Section: Local Existence and Global Existencementioning

confidence: 99%

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Global existence and bounds for blow‐up time in a class of nonlinear pseudo‐parabolic equations with a memory term

Luan

Yang

2019

Math Methods in App Sciences

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In this article, we consider the initial boundary value problem for a class of nonlinear pseudo‐parabolic equations with a memory term: ut−Δu−aΔut+∫0tg(t−s)Δu(x,s)ds+bu=normalΔpu+k(t)|ufalse|q−2u. Under suitable assumptions, we obtain the local and global existence of the solution by Galerkin method. We prove finite‐time blow‐up of the solution for initial data at arbitrary energy level and obtain upper bounds for blow‐up time by using the concavity method. In addition, by means of differential inequality technique, we obtain a lower bound for blow‐up time of the solution if blow‐up occurs.

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“…Next, by (A3), Gagliardo-Nirenberg interpolation inequality (see Nhan and Truong 16 and He te al 17 ) and Young inequality, we obtain…”

Section: Local Existence and Global Existencementioning

confidence: 87%

“…Firstly, we construct an approximate weak solution of the problem via Galerkin method (see other works()). In the space

W_{0}^{1, p} false(normalΩ false),

we take an orthogonal basis

{false{ω_{j} false}}_{j = 1}^{\infty}

.…”

Section: Local Existence and Global Existencementioning

confidence: 99%

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Global existence and bounds for blow‐up time in a class of nonlinear pseudo‐parabolic equations with a memory term

Luan

Yang

2019

Math Methods in App Sciences

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“…Ji, Yin and Cao [8] established the existence of positive periodic solutions and discussed the instability of such solutions for the semilinear pseudo-parabolic equation with the logarithmic source. Nahn and Truong [9] studied the following nonlinear equation: They obtained results as regards the existence or non-existence of global weak solutions. He, Gao and Wang [10] considered the following equation: where , they proved the decay and the finite time blow-up for weak solutions.…”

Section: Introductionmentioning

confidence: 99%

A class of fourth-order parabolic equation with logarithmic nonlinearity

Liu

2018

J Inequal Appl

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“…They applied the potential well method and logarithmic Sobolev inequality to prove the existence and nonexistence of global solutions as well as the asymptotic behavior of solutions. Later, the following pseudo-parabolic p-Laplacian evolution equation with logarithmic sources has been discussed: u t − ∆u t − div(|∇u| p−2 ∇u) = |u| q−2 u log |u| the interested readers can refer to [3], [4] and [15] for more details. Some existence or nonexistence of global solutions and the long time behavior of solutions are obtained under different assumptions about the initial data and the exponents.…”

mentioning

confidence: 99%

Bounds for lifespan of solutions to strongly damped semilinear wave equations with logarithmic sources and arbitrary initial energy

Zu¹,

Guo²

2021

Evolution Equations &Amp; Control Theory

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The main aim of this paper is to deal with the upper and lower bounds for blow-up time of solutions to the following equation:which has been studied in [5]. For high initial energy, it is well known that the classical potential well method is not effective. In order to overcome this difficulty, the authors apply the new energy estimate method to establish the lower bound of the L 2 (Ω) norm of the solution. Furthermore, the authors construct a new control functional and combine energy inequalities with the concavity argument to prove that the solution blows up in finite time for high initial energy. Meanwhile, an estimate of the upper bound of blow-up time is also obtained. Finally, a lower bound for blow-up time is obtained by introducing a new control functional. These results fill the gap of [5].

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Global solution and blow-up for a class of pseudo p-Laplacian evolution equations with logarithmic nonlinearity

Cited by 75 publications

References 20 publications

Global existence and bounds for blow‐up time in a class of nonlinear pseudo‐parabolic equations with a memory term

Global existence and bounds for blow‐up time in a class of nonlinear pseudo‐parabolic equations with a memory term

A class of fourth-order parabolic equation with logarithmic nonlinearity

Bounds for lifespan of solutions to strongly damped semilinear wave equations with logarithmic sources and arbitrary initial energy

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