On the Blowing-Up Of The Classical Solution For The Wave Equation With A Non Linear Source

2013 ◽  
Vol 2013 (1) ◽  
pp. 18
Author(s):  
Halima Nachid ◽  
Keyword(s):  
Wave Equation ◽  
Classical Solution ◽  
Linear Source ◽  
Blowing Up ◽  
Non Linear

scholarly journals Born-Infeld and charged black holes with non-linear source inf(T) gravity

2015 ◽  
Vol 2015 (06) ◽  
pp. 037-037 ◽  
Author(s):  
Ednaldo L.B. Junior ◽  
Manuel E. Rodrigues ◽  
Mahouton J.S. Houndjo
Keyword(s):  
Black Holes ◽  
Linear Source ◽  
Charged Black Holes ◽  
Non Linear

scholarly journals Solutions with Prescribed Local Blow-up Surface for the Nonlinear Wave Equation

2019 ◽  
Vol 19 (4) ◽  
pp. 639-675
Author(s):  
Thierry Cazenave ◽  
Yvan Martel ◽  
Lifeng Zhao
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Blow Up ◽  
Finite Energy ◽  
Energy Solution ◽  
Compact Set ◽  
Existence Of A Solution ◽  
Blowing Up ◽  
Finite Energy Solution

AbstractWe prove that any sufficiently differentiable space-like hypersurface of {{\mathbb{R}}^{1+N}} coincides locally around any of its points with the blow-up surface of a finite-energy solution of the focusing nonlinear wave equation {\partial_{tt}u-\Delta u=|u|^{p-1}u} on {{\mathbb{R}}\times{\mathbb{R}}^{N}}, for any {1\leq N\leq 4} and {1<p\leq\frac{N+2}{N-2}}. We follow the strategy developed in our previous work (2018) on the construction of solutions of the nonlinear wave equation blowing up at any prescribed compact set. Here to prove blow-up on a local space-like hypersurface, we first apply a change of variable to reduce the problem to blowup on a small ball at {t=0} for a transformed equation. The construction of an appropriate approximate solution is then combined with an energy method for the existence of a solution of the transformed problem that blows up at {t=0}. To obtain a finite-energy solution of the original problem from trace arguments, we need to work with {H^{2}\times H^{1}} solutions for the transformed problem.

Solitary dynamics of longitudinal wave equation arises in magneto-electro-elastic circular rod

2020 ◽  
pp. 2150086 ◽  
Author(s):  
Naila Sajid ◽  
Ghazala Akram
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Mapping Method ◽  
Integration Scheme ◽  
Auxiliary Equation ◽  
New Exact Solutions ◽  
Non Linear ◽  
Physical Phenomena

This paper examines the effectiveness of an integration scheme, which called the extended modified auxiliary equation mapping method in exactly solving a well-known non-linear longitudinal wave equation with dispersion caused by transverse Poisson’s effect arises in a magneto-electro-elastic (MEE) circular rod. Explicit new exact solutions are derived in different form such as hyperbolic, kinky, anti-kinky, dark, and singular solitons of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena.

scholarly journals Non-Singular Charged Black Hole Solution for Non-Linear Source

1999 ◽  
Vol 31 (5) ◽  
pp. 629-633 ◽  
Author(s):  
Eloy Ayon-Beato ◽  
Alberto Garcia
Keyword(s):  
Black Hole ◽  
Black Hole Solution ◽  
Charged Black Hole ◽  
Linear Source ◽  
Non Linear
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