scholarly journals A Class of Blow-Up Solution with External Diffusion and Nonlinear Boundary Flow Problems

2017 ◽  
Vol 06 (08) ◽  
pp. 975-984
Author(s):  
颖韬 李
Keyword(s):  
Nonlinear Boundary ◽  
Blow Up ◽  
Boundary Flow ◽  
Flow Problems ◽  
External Diffusion

Global existence, nonexistence, and decay of solutions for a wave equation of p-Laplacian type with weak and p-Laplacian damping, nonlinear boundary delay and source terms

2021 ◽  
pp. 1-16
Author(s):  
Nouri Boumaza ◽  
Billel Gheraibia
Keyword(s):  
Global Existence ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Source Terms ◽  
Delay Term ◽  
Laplacian Equation ◽  
Decay Of Solutions

In this paper, we consider the initial boundary value problem for the p-Laplacian equation with weak and p-Laplacian damping terms, nonlinear boundary, delay and source terms acting on the boundary. By introducing suitable energy and perturbed Lyapunov functionals, we prove global existence, finite time blow up and asymptotic behavior of solutions in cases p > 2 and p = 2. To our best knowledge, there is no results of the p-Laplacian equation with a nonlinear boundary delay term.

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