Title of article :
On the nonlinear wave equation
Ut t − B(t, Ux 2)Uxx = f (x, t,U,Ux,Ut , Ux 2)
associated with the mixed nonhomogeneous
conditions
Abstract :
In this paper we consider the following nonlinear wave equation
ut t −B t, ux 2 uxx = f x, t,u,ux,ut , ux 2 , x∈ Ω = (0, 1), 0 < t 0, B1 ∈
C2(R2+
), B1 0, f ∈ C3([0, 1]×R+ ×R3 ×R+) and f1 ∈ C2([0, 1]×R+ ×R3 ×R+) we obtain
from the equation ut t −[B(t, ux 2)+εB1(t , ux 2)]uxx = f (x, t,u,ux,ut , ux 2)+εf1(x, t,u,
ux,ut , ux 2) associated to (2), (3) a weak solution uε(x, t ) having an asymptotic expansion of
order 3 in ε, for ε sufficiently small.
2004 Elsevier Inc. All rights reserved
