scholarly journals Self-similar solutions of semilinear wave equation with variable speed of propagation

2007 ◽  
Vol 336 (2) ◽  
pp. 1259-1286 ◽  
Author(s):  
Karen Yagdjian
Keyword(s):  
Wave Equation ◽  
Variable Speed ◽  
Semilinear Wave Equation ◽  
Self Similar ◽  
Speed Of Propagation ◽  
Similar Solutions

ASYMPTOTICALLY SELF-SIMILAR GLOBAL SOLUTIONS OF A DAMPED WAVE EQUATION

2007 ◽  
Vol 09 (02) ◽  
pp. 253-277 ◽  
Author(s):  
SEIFEDDINE SNOUSSI ◽  
SLIM TAYACHI
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Global Solutions ◽  
The Self ◽  
Initial Condition ◽  
Damped Wave Equation ◽  
Small Initial Data ◽  
Additional Hypothesis ◽  
Self Similar ◽  
Similar Solutions

We study the existence and the asymptotic behavior of global solutions of the damped wave equation [Formula: see text] where a ∈ ℝ, α >1, t > 0, x ∈ ℝn, n = 1,2,3, with initial condition (u (0), ut (0)) = (φ,ψ). For α > 2 and α > 1+2 / n, we prove the existence of mild global solutions for small initial data with low regularity and which are not in L1(ℝn). Under the additional hypothesis, (2 < α < 5, when n = 3), we prove that some of these solutions are asymptotic to the self-similar solutions of the associated semi-linear heat equation [Formula: see text] with homogeneous slowly decreasing initial data behaving like c|x|-2 / (α-1) as |x|→ ∞.

ON SELF-SIMILAR SOLUTIONS, WELL-POSEDNESS AND THE CONFORMAL WAVE EQUATION

2002 ◽  
Vol 04 (02) ◽  
pp. 211-222 ◽  
Author(s):  
FABRICE PLANCHON
Keyword(s):  
Wave Equation ◽  
Linear Wave ◽  
Well Posedness ◽  
Initial Value ◽  
Linear Wave Equation ◽  
Conformally Invariant ◽  
Self Similar ◽  
Similar Solutions ◽  
Well Posed ◽  
Homogeneous Data

We prove that the initial value problem for the conformally invariant semi-linear wave equation is well-posed in the Besov space [Formula: see text]. This induces the existence of (non-radially symmetric) self-similar solutions for homogeneous data in such Besov spaces.

scholarly journals Self-similar solutions of the cubic wave equation

Nonlinearity ◽  
2010 ◽  
Vol 23 (2) ◽  
pp. 225-236 ◽  
Author(s):  
P Bizoń ◽  
P Breitenlohner ◽  
D Maison ◽  
A Wasserman
Keyword(s):  
Wave Equation ◽  
Self Similar ◽  
Similar Solutions

scholarly journals Dynamical behavior of the strong dispersive nonlinear wave equation

2021 ◽  
Vol XXII C ◽  
pp. 3-11
Author(s):  
Mehmed Kodzha
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Dynamical Behavior ◽  
The Self ◽  
Self Similar ◽  
Similar Solutions

In this paper we consider the dynamical behavior of solutions near explicit self-similar solutions for a strong dispersive nonlinear wave equation. First we construct explicit self-similar solutions, then we investigate dynamical behavior of the solutions near to the self-similar solutions.

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