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 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.

Blow-up of solutions for a Kirchhoff type equation with variable-exponent nonlinearities

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammad Shahrouzi ◽  
Firoozeh Kargarfard
Keyword(s):  
Variable Exponent ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Blow Up ◽  
Type Equation ◽  
Initial Energy ◽  
Kirchhoff Type ◽  
Positive Initial Energy ◽  
Kirchhoff Type Equation ◽  
Upper Bound Estimate

AbstractThis paper deals with a Kirchhoff type equation with variable exponent nonlinearities, subject to a nonlinear boundary condition. Under appropriate conditions and regarding arbitrary positive initial energy, it is proved that solutions blow up in a finite time. Moreover, we obtain the upper bound estimate of the blow-up time.

scholarly journals General decay and blow up of solutions for a variable-exponent viscoelastic double-Kirchhoff type wave equation with nonlocal degenerate damping

2021 ◽  
Author(s):  
Mohammad Shahrouzi ◽  
Jorge Ferreira ◽  
Erhan Pişkin
Keyword(s):  
Wave Equation ◽  
Variable Exponent ◽  
Blow Up ◽  
Type Equation ◽  
Initial Energy ◽  
General Decay ◽  
Kirchhoff Type ◽  
Type Wave ◽  
Positive Initial Energy ◽  
Viscoelastic Term

In this paper we consider a viscoelastic double-Kirchhoff type wave equation of the form $$ u_{tt}-M_{1}(\|\nabla u\|^{2})\Delta u-M_{2}(\|\nabla u\|_{p(x)})\Delta_{p(x)}u+(g\ast\Delta u)(x,t)+\sigma(\|\nabla u\|^{2})h(u_{t})=\phi(u), $$ where the functions $M_{1},M_{2}$ and $\sigma, \phi$ are real valued functions and $(g\ast\nabla u)(x,t)$ is the viscoelastic term which are introduced later. Under appropriate conditions for the data and exponents, the general decay result and blow-up of solutions are proved with positive initial energy. This study extends and improves the previous results in the literature to viscoelastic double-Kirchhoff type equation with degenerate nonlocal damping and variable-exponent nonlinearities.

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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