Global asymptotical behavior of solutions to a class of fourth order parabolic equation modeling epitaxial growth

Zhou, Jun

doi:10.1016/j.nonrwa.2019.01.001

Cited by 30 publications

(21 citation statements)

References 7 publications

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“…In details, we refer to Zhou et. al [10,37] for the p-Laplace equation, Han et. al [13,17] for the Kirchhoff equation, Su and Xu [32] for the pseudo-parabolic equation with localized source and arbitrary initial energy.…”

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confidence: 99%

Initial boundary value problem of a class of mixed pseudo-parabolic Kirchhoff equations

Cao

Zhao

2021

era

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<p style='text-indent:20px;'>In this paper, we consider the initial boundary value problem for a mixed pseudo-parabolic Kirchhoff equation. Due to the comparison principle being invalid, we use the potential well method to give a threshold result of global existence and non-existence for the sign-changing weak solutions with initial energy <inline-formula><tex-math id="M1">\begin{document}$ J(u_0)\leq d $\end{document}</tex-math></inline-formula>. When the initial energy <inline-formula><tex-math id="M2">\begin{document}$ J(u_0)>d $\end{document}</tex-math></inline-formula>, we find another criterion for the vanishing solution and blow-up solution. Our interest also lies in the discussion of the exponential decay rate of the global solution and life span of the blow-up solution.</p>

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confidence: 99%

Initial boundary value problem of a class of mixed pseudo-parabolic Kirchhoff equations

Cao

Zhao

2021

era

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“…In this section, we investigate the conditions that ensure the global existence or finite time blowingup of solution to (1.1). Inspired by the ideas in [18,25,37,38], we need to introduce some new notations. For a positive constant σ > d, we let…”

Section: )mentioning

confidence: 99%

Initial boundary value problem of pseudo-parabolic Kirchhoff equations with logarithmic nonlinearity

Cao

Zhao

2022

Preprint

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In this paper, we consider the initial boundary value problem for a pseudo-parabolic Kirchhoff equation with logarithmic nonlinearity. Using the potential well method, we obtain a threshold result of global existence and finite-time blow-up for the weak solutions with initial energy J ( u 0 ) ≤ d . When the initial energy J ( u 0 ) > d , we find another criterion for the vanishing solution and blow-up solution. We also establish the decay rate of the global solution and estimate the life span of the blow-up solution. Meanwhile, we study the existence of the ground state solution to the corresponding stationary problem.

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“…In this section, we investigate the conditions that ensure the global existence or finite time blowing-up of solution to (1.1). Inspired by the ideas in [21,28,30,33], we first introduce the following sets.…”

Section: Decay Rate and Life Spanmentioning

confidence: 99%

“…From many previous works about the IBVP of Kirchhoff equations, pseudo-parabolic equations and other parabolic equations, the global solutions converge to 0 as t tends to ∞ when the initial data satisfies some special conditions. Recently, some mathematicians [28,31] make further discussion on the asymptotic behavior of general global solutions and find that it is relevant to the ground state solutions of the stationary problem.…”

Section: Introductionmentioning

confidence: 99%

Initial boundary value problem of a class of pseudo-parabolic Kirchhoff equations with logarithmic nonlinearity

Zhao

2021

Preprint

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In this paper, we consider the initial boundary value problem for a pseudoparabolic Kirchhoff equation with logarithmic nonlinearity. We use the potential well method to give a threshold result of global existence and finite-time blow-up for the weak solutions with initial energy J(u 0 ) ≤ d. When the initial energy J(u 0 ) > d, we find another criterion for the vanishing solution and blow-up solution. We also get the exponential decay rate of the global solution and life span of the blow-up solution. Meanwhile, we study the corresponding stationary problem and establish a convergence relationship between its ground state solution and the global solution.

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Global asymptotical behavior of solutions to a class of fourth order parabolic equation modeling epitaxial growth

Cited by 30 publications

References 7 publications

Initial boundary value problem of a class of mixed pseudo-parabolic Kirchhoff equations

Initial boundary value problem of a class of mixed pseudo-parabolic Kirchhoff equations

Initial boundary value problem of pseudo-parabolic Kirchhoff equations with logarithmic nonlinearity

Initial boundary value problem of a class of pseudo-parabolic Kirchhoff equations with logarithmic nonlinearity

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