New results on Blow-up of solutions for Emden-Fowler type degenerate wave equation with memory

2021 ◽  
Vol 39 (2) ◽  
pp. 163-179
Author(s):  
Khaled Zennir ◽  
Svetlin G. Georgiev
Keyword(s):  
Wave Equation ◽  
Relaxation Function ◽  
Blow Up ◽  
Global Solutions ◽  
Degenerate Problem ◽  
New Class ◽  
Dissipative Case ◽  
With Memory ◽  
Degenerate Wave Equation

In this article we consider a new class of a Emden-Fowler type semilinear degenerate wave equation with memory. The main contributions here is to show that the memory lets the global solutions of the degenerate problem still non-exist without any conditions on the nature of growth of the relaxation function. This is to extend the paper in \cite{L11} for the dissipative case.

Global solutions and finite time blow-up for fourth order nonlinear damped wave equation

2018 ◽  
Vol 59 (6) ◽  
pp. 061503 ◽  
Author(s):  
Runzhang Xu ◽  
Xingchang Wang ◽  
Yanbing Yang ◽  
Shaohua Chen
Keyword(s):  
Wave Equation ◽  
Fourth Order ◽  
Finite Time ◽  
Blow Up ◽  
Global Solutions ◽  
Damped Wave Equation ◽  
Nonlinear Damped Wave Equation

scholarly journals A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivative-type in the generalized Einstein-de Sitter spacetime

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Makram Hamouda ◽  
Mohamed Ali Hamza ◽  
Alessandro Palmieri
Keyword(s):  
Wave Equation ◽  
Blow Up ◽  
Integral Transform ◽  
Global Solutions ◽  
Representation Formula ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Semilinear Wave Equation ◽  
Sitter Spacetime ◽  
Derivative Type

<p style='text-indent:20px;'>In this paper, we establish blow-up results for the semilinear wave equation in generalized Einstein-de Sitter spacetime with nonlinearity of derivative type. Our approach is based on the integral representation formula for the solution to the corresponding linear problem in the one-dimensional case, that we will determine through Yagdjian's Integral Transform approach. As upper bound for the exponent of the nonlinear term, we discover a Glassey-type exponent which depends both on the space dimension and on the Lorentzian metric in the generalized Einstein-de Sitter spacetime.</p>

scholarly journals Global solutions and general decay for the dispersive wave equation with memory and source terms

2020 ◽  
Vol 4 (2) ◽  
pp. 116-122
Author(s):  
Mohamed Mellah ◽  
Keyword(s):  
Wave Equation ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
General Decay ◽  
Dispersive Wave ◽  
Source Terms ◽  
Initial Boundary Value ◽  
With Memory ◽  
Dispersive Wave Equation

This paper concerns with the global solutions and general decay to an initial-boundary value problem of the dispersive wave equation with memory and source terms

Existence and blow-up of a new class of nonlinear damped wave equation

2020 ◽  
Vol 38 (3) ◽  
pp. 2649-2660
Author(s):  
Zakia Tebba ◽  
Salah Boulaaras ◽  
Hakima Degaichia ◽  
Ali Allahem
Keyword(s):  
Wave Equation ◽  
Blow Up ◽  
Damped Wave Equation ◽  
New Class ◽  
Nonlinear Damped 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).

scholarly journals General decay of the double dispersive wave equation with memory and source terms

2021 ◽  
Vol 5 (1) ◽  
pp. 1-8
Author(s):  
Mohamed Mellah ◽  
Keyword(s):  
Wave Equation ◽  
Bounded Domain ◽  
Global Solutions ◽  
Decay Rates ◽  
General Decay ◽  
Dispersive Wave ◽  
Source Terms ◽  
T Tau ◽  
With Memory ◽  
Dispersive Wave Equation

The double dispersive wave equation with memory and source terms \(u_{tt}-\Delta u-\Delta u_{tt}+\Delta^{2}u-\int_{0}^{t}g(t-\tau)\Delta^{2}u(\tau)d\tau-\Delta u_{t}=|u|^{p-2}u \) is considered in bounded domain. The existence of global solutions and decay rates of the energy are proved.

scholarly journals General decay and blow-up of solutions for a nonlinear wave equation with memory and fractional boundary damping terms

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Salah Boulaaras ◽  
Fares Kamache ◽  
Youcef Bouizem ◽  
Rafik Guefaifia
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Lyapunov Functional ◽  
Blow Up ◽  
Initial Energy ◽  
General Decay ◽  
Memory Term ◽  
Decay Of Solutions ◽  
With Memory

AbstractThe paper studies the global existence and general decay of solutions using Lyapunov functional for a nonlinear wave equation, taking into account the fractional derivative boundary condition and memory term. In addition, we establish the blow-up of solutions with nonpositive initial energy.

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