Global Existence and Exponential Decay for a Nonlinear Viscoelastic Equation with Nonlinear Damping

2009 ◽  
Vol 22 (4) ◽  
pp. 299-314 ◽  
Author(s):  
Han Xiaosen
Keyword(s):  
Global Existence ◽  
Exponential Decay ◽  
Nonlinear Damping ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equation

scholarly journals Global Nonexistence for a Nonlinear Viscoelastic Equation with Nonlinear Damping and Velocity-Dependent Material Density

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Jian Dang ◽  
Qingying Hu ◽  
Hongwei Zhang
Keyword(s):  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Damping ◽  
Initial Energy ◽  
Material Density ◽  
Nonexistence Result ◽  
Nonlinear Viscoelastic ◽  
Global Nonexistence ◽  
Viscoelastic Equation

We consider the initial boundary value problem of a nonlinear viscoelastic equation of Kirchhoff-type with nonlinear damping and velocity-dependent material density. We establish a nonexistence result of global solutions with positive initial energy and negative initial energy, respectively.

Optimal decay of an abstract nonlinear viscoelastic equation in Hilbert spaces with delay term in the nonlinear internal damping

2020 ◽  
pp. 1-30
Author(s):  
Houria Chellaoua ◽  
Yamna Boukhatem ◽  
Baowei Feng
Keyword(s):  
Hilbert Spaces ◽  
Nonlinear Damping ◽  
Delayed Feedback ◽  
Internal Damping ◽  
General Decay Rate ◽  
Delay Term ◽  
Nonlinear Viscoelastic ◽  
Optimal Decay ◽  
Viscoelastic Equation ◽  
Nonlinear Internal Damping

In this paper, we consider a second-order abstract viscoelastic equation in Hilbert spaces with delay term in the nonlinear internal damping and a nonlinear source term. Under some suitable assumptions on the weight of the delayed feedback, the weight of the non-delayed feedback and the behavior of the relaxation function, we establish two explicit and general decay rate results of the energy by introducing a suitable Lyaponov functional and some properties of the convex functions. Moreover, we give some applications and examples. This work generalizes the previous results without time delay term to those with delay in the nonlinear damping.

GLOBAL SMOOTH SOLUTION AND UNIFORM RATE OF DECAY IN NONLINEAR VISCOELASTICITY

1994 ◽  
Vol 06 (05) ◽  
pp. 855-868 ◽  
Author(s):  
JAIME E. MUÑOZ RIVERA
Keyword(s):  
Global Existence ◽  
Existence Theorem ◽  
Smooth Solution ◽  
Nonlinear Viscoelasticity ◽  
Small Data ◽  
Bounded Domains ◽  
Nonlinear Viscoelastic ◽  
Global Existence Theorem ◽  
Viscoelastic Equation ◽  
Rate Of Decay

We prove a global existence theorem for the nonlinear viscoelastic equation for small data in H2. Moreover we prove that the solution decays exponentially in bounded domains when t goes to infinity.

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