scholarly journals A class of diffusion problem of Kirchhoff type with viscoelastic term involving the fractional Laplacian

2020 ◽  
Vol 65 (4) ◽  
pp. 543-559
Author(s):  
Eugenio Cabanillas L. ◽  
Zacarias Huaringa Segura ◽  
Juan B. Bernui Barros ◽  
Eduardo V. Trujillo Flores
Keyword(s):  
Exponential Decay ◽  
Fractional Laplacian ◽  
Global Solutions ◽  
Diffusion Problem ◽  
Kirchhoff Type ◽  
Viscoelastic Term

This work is concerned with a class of diffusion problem of Kirchhoff type with viscoelastic term and nonlinear interior source in the setting of the fractional Laplacian. Under suitable conditions we prove the existence of global solutions and the exponential decay of the energy.

scholarly journals Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Daewook Kim ◽  
Dojin Kim ◽  
Keum-Shik Hong ◽  
Il Hyo Jung
Keyword(s):  
Wave Equation ◽  
Existence And Uniqueness ◽  
Global Solutions ◽  
Growth Conditions ◽  
Decay Rates ◽  
Decay Estimates ◽  
Nonlinear Dissipation ◽  
Kirchhoff Type ◽  
Type Wave ◽  
Energy Decay Rates

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form under suitable assumptions on . Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipationg. Lastly, numerical simulations in order to verify the analytical results are given.

scholarly journals A diffusion problem of Kirchhoff type involving the nonlocal fractional $p$--Laplacian

2017 ◽  
Vol 37 (7) ◽  
pp. 4035-4051 ◽  
Author(s):  
Binlin Zhang ◽  
Mingqi Xiang ◽  
Patrizia Pucci
Keyword(s):  
Diffusion Problem ◽  
Kirchhoff Type

scholarly journals Exponential decay of solutions of a semilinear Lipschitz Perturbation of Kirchhoff-Carrier Wave Equation

1993 ◽  
Vol 15 (15) ◽  
pp. 17
Author(s):  
Eleni Bisognin
Keyword(s):  
Wave Equation ◽  
Mixed Problem ◽  
Exponential Decay ◽  
Lipschitz Function ◽  
Global Solutions ◽  
Work Study ◽  
Carrier Wave ◽  
Decay Of Solutions ◽  
Lipschitz Perturbation

In this work study the existence of global solutions and exponential decay of energy of the mixed problem for perturbed Kirchhoff-Carrier wave equationu" - M(a(u)) Δu + F(u) + γ u’ = fwhere F is a Lipschitz function.

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