scholarly journals Blow-up results for a quasilinear von Karman equation of memory type

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Mi Jin Lee ◽  
Jum-Ran Kang
Keyword(s):  
Blow Up ◽  
Suitable Condition ◽  
Nondecreasing Function ◽  
Initial Energy ◽  
Nonincreasing Function ◽  
Positive Initial Energy ◽  
Von Karman ◽  
Von Karman Equation ◽  
Memory Type ◽  
Von Kármán

Abstract In this paper, we consider the blow-up result of solution for a quasilinear von Karman equation of memory type with nonpositive initial energy as well as positive initial energy. For nonincreasing function $g>0$ g > 0 and nondecreasing function f, we prove a finite time blow-up result under suitable condition on the initial data.

scholarly journals Blow-up for a viscoelastic von Karman equation with strong damping and variable exponent source terms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sun-Hye Park
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Variable Exponent ◽  
Blow Up ◽  
Initial Energy ◽  
Positive Initial Energy ◽  
Von Karman ◽  
Von Karman Equation ◽  
Von Kármán ◽  
Strongly Damped

AbstractIn this article, we deal with a strongly damped von Karman equation with variable exponent source and memory effects. We investigate blow-up results of solutions with three levels of initial energy such as non-positive initial energy, certain positive initial energy, and high initial energy. Furthermore, we estimate not only the upper bound but also the lower bound of the blow-up time.

scholarly journals Energy Decay for a Von Karman Equation of Memory Type with a Delay Term

2017 ◽  
Vol 05 (09) ◽  
pp. 1797-1807 ◽  
Author(s):  
Sun-Hye Park ◽  
Jong-Yeoul Park ◽  
Yong-Han Kang
Keyword(s):  
Energy Decay ◽  
Delay Term ◽  
Von Karman ◽  
Von Karman Equation ◽  
Memory Type ◽  
Von Kármán

scholarly journals Global existence and nonexistence for a class of finitely degenerate coupled parabolic systems with high initial energy level

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yuxuan Chen ◽  
Jiangbo Han
Keyword(s):  
Energy Level ◽  
Global Existence ◽  
Blow Up ◽  
Parabolic Systems ◽  
Initial Energy ◽  
Blowup Time ◽  
Positive Initial Energy ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions ◽  
Coupled Parabolic Systems

<p style='text-indent:20px;'>In this paper, we consider a class of finitely degenerate coupled parabolic systems. At high initial energy level <inline-formula><tex-math id="M1">\begin{document}$ J(u_{0})&gt;d $\end{document}</tex-math></inline-formula>, we present a new sufficient condition to describe the global existence and nonexistence of solutions for problem (1)-(4) respectively. Moreover, by applying the Levine's concavity method, we give some affirmative answers to finite time blow up of solutions at arbitrary positive initial energy <inline-formula><tex-math id="M2">\begin{document}$ J(u_{0})&gt;0 $\end{document}</tex-math></inline-formula>, including the estimate of upper bound of blowup time.</p>

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