Affiliation:
1. Department of Mathematics , College of Science , King Saud University , P.O. Box 2455 , Riyadh 11451 , Saudi Arabia
Abstract
Abstract
In the paper, we study a Balakrishnan–Taylor quasilinear wave equation
|
z
t
|
α
z
t
t
-
Δ
z
t
t
-
(
ξ
1
+
ξ
2
∥
∇
z
∥
2
+
σ
(
∇
z
,
∇
z
t
)
)
Δ
z
-
Δ
z
t
+
β
(
x
)
f
(
z
t
)
+
g
(
z
)
=
0
|z_{t}|^{\alpha}z_{tt}-\Delta z_{tt}-\bigl{(}\xi_{1}+\xi_{2}\|\nabla z\|^{2}+%
\sigma(\nabla z,\nabla z_{t})\bigr{)}\Delta z-\Delta z_{t}+\beta(x)f(z_{t})+g(%
z)=0
in a bounded domain of
ℝ
n
{\mathbb{R}^{n}}
with Dirichlet boundary conditions. By using Faedo–Galerkin method, we prove the existence of global weak solutions. By the help of the perturbed energy method, the exponential stability of solutions is also established.
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