On the decay of solutions of a damped quasilinear wave equation with variable‐exponent nonlinearities

2020 ◽  
Vol 43 (8) ◽  
pp. 5114-5126 ◽  
Author(s):  
Salim A. Messaoudi
Keyword(s):  
Wave Equation ◽  
Variable Exponent ◽  
Quasilinear Wave Equation ◽  
Decay Of Solutions

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).

Decay of solutions of the wave equation outside nontrapping obstacles

1977 ◽  
Vol 30 (4) ◽  
pp. 447-508 ◽  
Author(s):  
Cathleen S. Morawetz ◽  
James V. Ralston ◽  
Walter A. Strauss
Keyword(s):  
Wave Equation ◽  
Decay Of Solutions
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