Blowup in solutions of a quasilinear wave equation with variable-exponent nonlinearities

2017 ◽  
Vol 40 (18) ◽  
pp. 6976-6986 ◽  
Author(s):  
Salim A. Messaoudi ◽  
Ala A. Talahmeh
Keyword(s):  
Wave Equation ◽  
Variable Exponent ◽  
Quasilinear Wave Equation

scholarly journals Blow-Up of Solutions for a Class Quasilinear Wave Equation with Nonlinearity Variable Exponents

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zakia Tebba ◽  
Hakima Degaichia ◽  
Mohamed Abdalla ◽  
Bahri Belkacem Cherif ◽  
Ibrahim Mekawy
Keyword(s):  
Wave Equation ◽  
Finite Time ◽  
Variable Exponent ◽  
Blow Up ◽  
Initial Energy ◽  
Positive Energy ◽  
Variable Exponents ◽  
Quasilinear Wave Equation ◽  
New Class ◽  
Dispersion Term

This work deals with the blow-up of solutions for a new class of quasilinear wave equation with variable exponent nonlinearities. To clarify more, we prove in the presence of dispersion term − Δ u t t a finite-time blow-up result for the solutions with negative initial energy and also for certain solutions with positive energy. Our results are extension of the recent work (Appl Anal. 2017; 96(9): 1509-1515).

The Quasilinear Wave Equation for Antiplane Shearing of Nonlinearly Elastic Bodies

2001 ◽  
Vol 171 (1) ◽  
pp. 201-226 ◽  
Author(s):  
Dawn A. Lott ◽  
Stuart S. Antman ◽  
William G. Szymczak
Keyword(s):  
Wave Equation ◽  
Quasilinear Wave Equation ◽  
Elastic Bodies ◽  
Nonlinearly Elastic
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