GLOBAL EXISTENCE, DECAY AND BLOW-UP OF SOLUTIONS FOR THE HIGHER-ORDER NONLINEAR KIRCHHOFF TYPE EQUATION WITH A STRONG DISSIPATION

2017 ◽  
Vol 29 (1) ◽  
pp. 37-76
Author(s):  
Guoguang Lin ◽  
Yunlong Gao ◽  
Yuting Sun
Keyword(s):  
Global Existence ◽  
Blow Up ◽  
Type Equation ◽  
Higher Order ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation

scholarly journals Existence, Decay, and Blow-Up of Solutions for a Higher-Order Kirchhoff-Type Equation with Delay Term

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hazal Yüksekkaya ◽  
Erhan Pişkin ◽  
Salah Mahmoud Boulaaras ◽  
Bahri Belkacem Cherif
Keyword(s):  
Blow Up ◽  
Type Equation ◽  
Initial Boundary ◽  
Initial Energy ◽  
Higher Order ◽  
Delay Term ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Decay Of Solutions ◽  
Equation With Delay

This article deals with the study of the higher-order Kirchhoff-type equation with delay term in a bounded domain with initial boundary conditions, where firstly, we prove the global existence result of the solution. Then, we discuss the decay of solutions by using Nakao’s technique and denote polynomially and exponentially. Furthermore, the blow-up result is established for negative initial energy under appropriate conditions.

Blow-up of solutions for a Kirchhoff type equation with variable-exponent nonlinearities

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammad Shahrouzi ◽  
Firoozeh Kargarfard
Keyword(s):  
Variable Exponent ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Blow Up ◽  
Type Equation ◽  
Initial Energy ◽  
Kirchhoff Type ◽  
Positive Initial Energy ◽  
Kirchhoff Type Equation ◽  
Upper Bound Estimate

AbstractThis paper deals with a Kirchhoff type equation with variable exponent nonlinearities, subject to a nonlinear boundary condition. Under appropriate conditions and regarding arbitrary positive initial energy, it is proved that solutions blow up in a finite time. Moreover, we obtain the upper bound estimate of the blow-up time.

Sign in / Sign up

Export Citation Format

Share Document