Title of article :
Global attractor for a nonlocal hyperbolic problem on RN
Author/Authors :
Papadopoulos, P Department of Electronics Engineering - School of Technological Applications - Piraeus University of Applied Sciences (Technological Education Institute of Piraeus) - Egaleo - Athens, Greece , Matiadou, N.L Department of Electronics Engineering - School of Technological Applications - Piraeus University of Applied Sciences (Technological Education Institute of Piraeus) - Egaleo - Athens, Greece
Abstract :
We consider the quasilinear Kirchho's problem with the initial conditions u(x; 0) = u0(x) and ut(x; 0) = u1(x), in the case where N ≥ 3; f(u) =
jujau and (∅(x))-1 ∈ LN/2(RN) ∩ L∞(RN) is a positive function. The purpose of our work is to
study the long time behaviour of the solution of this equation. Here, we prove the existence of a
global attractor for this equation in the strong topology of the space X1 =: D1;2(RN)xL2g
(RN): We
succeed to extend some of our earlier results concerning the asymptotic behaviour of the solution of
the problem.
Keywords :
quasilinear hyperbolic equations , global attractor , generalised Sobolev spaces , weighted Lp Spaces
Journal title :
Astroparticle Physics
