Global Existence and Uniform Decay of Solutions for a Kirchhoff Beam Equation with Nonlinear Damping and Source Term

2021 ◽  
Author(s):  
Ducival C. Pereira ◽  
Carlos A. Raposo ◽  
Celsa H. M. Maranhão ◽  
Adriano P. Cattai
Keyword(s):  
Global Existence ◽  
Source Term ◽  
Nonlinear Damping ◽  
Beam Equation ◽  
Uniform Decay ◽  
Decay Of Solutions

scholarly journals Existence and uniform decay of solutions for a class of generalized plate-membrane-like systems

2006 ◽  
Vol 2006 ◽  
pp. 1-24
Author(s):  
Haihong Liu ◽  
Ning Su
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Nonlinear Damping ◽  
Asymptotic Behavior Of Solutions ◽  
Uniform Decay ◽  
Decay Of Solutions

We study the global existence, uniqueness, and asymptotic behavior of solutions for a class of generalized plate-membrane-like systems with nonlinear damping and source acting both interior and on boundary.

scholarly journals Global existence and blow-up results for a nonlinear model for a dynamic suspension bridge

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Quang-Minh Tran ◽  
Hong-Danh Pham
Keyword(s):  
Weak Solution ◽  
Global Existence ◽  
Decay Rate ◽  
Wave Equations ◽  
Source Term ◽  
Blow Up ◽  
Suspension Bridge ◽  
Nonlinear Damping ◽  
Damping Term ◽  
General Decay Rate

<p style='text-indent:20px;'>The paper deals with global existence and blow-up results for a class of fourth-order wave equations with nonlinear damping term and superlinear source term with the coefficient depends on space and time variable. In the case the weak solution is global, we give information on the decay rate of the solution. In the case the weak solution blows up in finite time, estimate the lower bound and upper bound of the lifespan of the blow-up solution, and also estimate the blow-up rate. Finally, if our problem contains an external vertical load term, a sufficient condition is also established to obtain the global existence and general decay rate of weak solutions.</p>

scholarly journals Global Existence, Asymptotic Behavior and Blow-up of Solutions for a Suspension Bridge Equation with Nonlinear Damping and Source Terms

2017 ◽  
Author(s):  
Wenjun Liu ◽  
Hefeng Zhuang
Keyword(s):  
Global Existence ◽  
Source Term ◽  
Blow Up ◽  
Suspension Bridge ◽  
Nonlinear Damping ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Damping Term ◽  
Necessary And Sufficient ◽  
Damping And Source Terms

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |ut|m-2ut and source term |u|p-2u. &nbsp;We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p&gt;m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time Tmax is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

Uniform decay rate estimates for the beam equation with locally distributed nonlinear damping

2021 ◽  
Author(s):  
Marcelo M. Cavalcanti ◽  
Leonel G. Delatorre ◽  
Valéria N. Domingos Cavalcanti ◽  
Victor H. Gonzalez Martinez ◽  
Daiane C. Soares
Keyword(s):  
Decay Rate ◽  
Nonlinear Damping ◽  
Beam Equation ◽  
Uniform Decay

scholarly journals Global Existence and Energy Decay of Solutions to a Petrovsky Equation with General Nonlinear Dissipation and Source Term

2006 ◽  
Vol 13 (3) ◽  
pp. 397-410 ◽  
Author(s):  
Nour-Eddine Amroun ◽  
Abbes Benaissa
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Polynomial Growth ◽  
Source Term ◽  
Stable Set ◽  
Asymptotic Behavior Of Solutions ◽  
Nonlinear Dissipation ◽  
Dissipative Term ◽  
Decay Of Solutions ◽  
Petrovsky Equation

Abstract We consider the nonlinearly damped semilinear Petrovsky equation and prove the global existence of its solutions by means of the stable set method in combined with the Faedo–Galerkin procedure. Furthermore, we study the asymptotic behavior of solutions when the nonlinear dissipative term 𝑔 does not necessarily have a polynomial growth near the origin.

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