FINITE TIME BLOW UP OF FOURTH-ORDER WAVE EQUATIONS WITH NONLINEAR STRAIN AND SOURCE TERMS AT HIGH ENERGY LEVEL

In this paper, we study the initial boundary value problem for fourth-order wave equations with nonlinear strain and source terms at high energy level. We prove that, for certain initial data in the unstable set, the solution with arbitrarily positive initial energy blows up in finite time.

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FINITE TIME BLOW-UP FOR THE NONLINEAR FOURTH-ORDER DISPERSIVE-DISSIPATIVE WAVE EQUATION AT HIGH ENERGY LEVEL

International Journal of Mathematics ◽

10.1142/s0129167x12500607 ◽

2012 ◽

Vol 23 (05) ◽

pp. 1250060 ◽

Cited By ~ 6

Author(s):

RUNZHANG XU ◽

YANBING YANG

Keyword(s):

Wave Equation ◽

Fourth Order ◽

Blow Up ◽

Initial Boundary ◽

Initial Boundary Value Problem ◽

High Energy ◽

Initial Energy ◽

High Energy Level ◽

Positive Initial Energy ◽

Dissipative Wave Equation

In this paper, we investigate the initial boundary value problem of the nonlinear fourth-order dispersive-dissipative wave equation. By using the concavity method, we establish a blow-up result for certain solutions with arbitrary positive initial energy.

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Finite Time Blow Up of Solution for 1-D Nonlinear Wave Equation of Sixth Order with Linear Restoring Force at High Energy Level

Journal of Partial Differential Equations ◽

10.4208/jpde.v31.n3.6 ◽

2018 ◽

Vol 31 (3) ◽

pp. 274-280

Author(s):

Yang Yanbing and Huang Shaobin

Keyword(s):

Wave Equation ◽

Energy Level ◽

Nonlinear Wave ◽

Nonlinear Wave Equation ◽

Finite Time ◽

Blow Up ◽

High Energy ◽

Sixth Order ◽

Restoring Force ◽

High Energy Level

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Finite time blow-up and global solutions for a class of semilinear parabolic equations at high energy level

Nonlinear Analysis Real World Applications ◽

10.1016/j.nonrwa.2011.07.025 ◽

2012 ◽

Vol 13 (1) ◽

pp. 197-202 ◽

Cited By ~ 7

Author(s):

Runzhang Xu ◽

Xiuying Cao ◽

Tao Yu

Keyword(s):

Energy Level ◽

Parabolic Equations ◽

Finite Time ◽

Blow Up ◽

Global Solutions ◽

High Energy ◽

Semilinear Parabolic Equations ◽

High Energy Level ◽

Semilinear Parabolic

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Finite time blow-up and global solutions for fourth order damped wave equations

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2014.04.015 ◽

2014 ◽

Vol 418 (2) ◽

pp. 713-733 ◽

Cited By ~ 19

Author(s):

Yongda Wang

Keyword(s):

Fourth Order ◽

Finite Time ◽

Wave Equations ◽

Blow Up ◽

Global Solutions

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On the initial–boundary problem for fourth order wave equations with damping, strain and source terms

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2013.03.060 ◽

2013 ◽

Vol 405 (1) ◽

pp. 116-127 ◽

Cited By ~ 9

Author(s):

Yanjin Wang ◽

Yufeng Wang

Keyword(s):

Boundary Problem ◽

Fourth Order ◽

Wave Equations ◽

Initial Boundary ◽

Source Terms ◽

Initial Boundary Problem

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Critical and sup-critical initial energy finite time blowup phenomena for the fourth-order wave equations with nonlinear strain term

Nonlinear Analysis ◽

10.1016/j.na.2020.111873 ◽

2020 ◽

Vol 198 ◽

pp. 111873

Author(s):

Qiang Lin ◽

Jihong Shen ◽

Xingchang Wang

Keyword(s):

Fourth Order ◽

Finite Time ◽

Wave Equations ◽

Initial Energy ◽

Nonlinear Strain ◽

Finite Time Blowup ◽

Time Blowup

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Fourth order wave equations with nonlinear strain and source terms

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.09.010 ◽

2007 ◽

Vol 331 (1) ◽

pp. 585-607 ◽

Cited By ~ 26

Author(s):

Yacheng Liu ◽

Runzhang Xu

Keyword(s):

Fourth Order ◽

Wave Equations ◽

Source Terms ◽

Nonlinear Strain

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Nonlinear wave equations and reaction-diffusion equations with several nonlinear source terms of different signs at high energy level

ANZIAM Journal ◽

10.21914/anziamj.v54i0.6468 ◽

2013 ◽

Vol 54 ◽

pp. 153

Author(s):

Runzhang Xu ◽

Yanbing Yang ◽

Shaohua Chen ◽

Jia Su ◽

Jihong Shen ◽

...

Keyword(s):

Energy Level ◽

Nonlinear Wave ◽

Wave Equations ◽

Reaction Diffusion ◽

High Energy ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Nonlinear Wave Equations ◽

Nonlinear Source ◽

High Energy Level

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Blow-up of solutions for a nonlinear Petrovsky type equation with initial data at arbitrary high energy level

Boundary Value Problems ◽

10.1186/s13661-019-1136-x ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 5

Author(s):

Lishan Liu ◽

Fenglong Sun ◽

Yonghong Wu

Keyword(s):

Energy Level ◽

Initial Data ◽

Blow Up ◽

Type Equation ◽

High Energy ◽

High Energy Level ◽

Petrovsky Type Equation

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A Class of Fourth Order Damped Wave Equations with Arbitrary Positive Initial Energy

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091518000330 ◽

2018 ◽

Vol 62 (1) ◽

pp. 165-178

Author(s):

Yang Liu ◽

Jia Mu ◽

Yujuan Jiao

Keyword(s):

Global Existence ◽

Boundary Value Problem ◽

Fourth Order ◽

Wave Equations ◽

Blow Up ◽

Initial Boundary ◽

Initial Boundary Value Problem ◽

Initial Energy ◽

Positive Initial Energy ◽

Initial Boundary Value

AbstractIn this paper, we study the initial boundary value problem for a class of fourth order damped wave equations with arbitrary positive initial energy. In the framework of the energy method, we further exploit the properties of the Nehari functional. Finally, the global existence and finite time blow-up of solutions are obtained.

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