Existence, blow-up, and exponential decay estimates for a system of semilinear wave equations associated with the helicalflows of Maxwell fluid

2015 ◽  
Vol 39 (9) ◽  
pp. 2334-2357
Author(s):  
Le Thi Phuong Ngoc ◽  
Cao Huu Hoa ◽  
Nguyen Thanh Long
Keyword(s):  
Exponential Decay ◽  
Wave Equations ◽  
Blow Up ◽  
Maxwell Fluid ◽  
Decay Estimates ◽  
Semilinear Wave Equations

scholarly journals Existence, blow-up and exponential decay estimates for the nonlinear Kirchhoff-Carrier wave equation in an annular with nonhomogeneous Dirichlet conditions

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5561-5588 ◽  
Author(s):  
le Son ◽  
Le Ngoc ◽  
Nguyen Long
Keyword(s):  
Wave Equation ◽  
Exponential Decay ◽  
Existence And Uniqueness ◽  
Lyapunov Functional ◽  
Blow Up ◽  
Initial Energy ◽  
Decay Estimates ◽  
Carrier Wave ◽  
Dirichlet Conditions ◽  
Uniqueness Of The Solution

This paper is devoted to the study of a nonlinear Kirchhoff-Carrier wave equation in an annular associated with nonhomogeneous Dirichlet conditions. At first, by applying the Faedo-Galerkin, we prove existence and uniqueness of the solution of the problem considered. Next, by constructing Lyapunov functional, we prove a blow-up result for solutions with a negative initial energy and establish a sufficient condition to obtain the exponential decay of weak solutions.

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