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Keywords
(10)
a priori estimate
Asymptotic Expansion
Boundary Condition
Existence and Uniqueness
galerkin method
Initial Boundary Value Problem
Nonlinear Wave Equation
Second Order Differential Equation
Cauchy Problem
Weak Solution
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On a nonlinear wave equation with boundary conditions involved in a Cauchy problem
On a nonlinear wave equation with boundary conditions involved in a Cauchy problem,10.1016/j.nonrwa.2010.05.036,Nonlinear Analysisreal World Applicat
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On a nonlinear wave equation with boundary conditions involved in a Cauchy problem
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Le Thi Phuong Ngoc
,
Le Khanh Luan
,
Tran Minh Thuyet
,
Nguyen Thanh Long
We consider the
initial boundary value problem
for the
nonlinear wave equation
utt−∂∂x(μ(x,t)ux)+Kup−2u+λutq−2ut=F(x,t),0x1,0tT, where the
boundary condition
at x=0 is associated with a secondorder
differential equation
P′′(t)+γ1P′(t)+γ2P(t)=β(t)utt(0,t),0tT, and the
boundary condition
at x=1 is of the form μ(1,t)ux(1,t)=λ1ut(1,t)α−2ut(1,t), where K,λ,p,q,γ1,γ2,λ1,α,p, and q are given positive constants, F,μ, and β are given functions. First, the
existence and uniqueness
of a
weak solution
are proved by using the Faedo–Galerkin method. Next, the asymptotic behavior of the solution as λ1→0+ is discussed. Finally, we obtain an
asymptotic expansion
of the solution up to order N in a small parameter λ1 with error λ1α(N+1)−12(α−1).
Journal:
Nonlinear Analysisreal World Applications  NONLINEAR ANALREAL WORLD APP
, vol. 12, no. 1, pp. 6992, 2011
DOI:
10.1016/j.nonrwa.2010.05.036
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References
(10)
Mathematical model for a shock problem involving a linear viscoelastic bar
(
Citations: 19
)
Nguyen Thanh Long
,
Alain Pham Ngoc Dinh
Journal:
Nonlinear Analysistheory Methods & Applications  NONLINEAR ANALTHEOR METH APP
, vol. 43, no. 5, pp. 547561, 2001
On a shock problem involving a linear viscoelastic bar
(
Citations: 18
)
Nguyen Thanh Long
,
Le Van Ut
,
Nguyen Thi Thao Truc
Journal:
Nonlinear Analysistheory Methods & Applications  NONLINEAR ANALTHEOR METH APP
, vol. 63, no. 2, pp. 198224, 2005
On existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions
(
Citations: 6
)
M. M. Cavalcanti
,
V. N. Domingos Cavalcanti
,
J. A. Soriano
Journal:
Journal of Mathematical Analysis and Applications  J MATH ANAL APPL
, vol. 281, no. 1, pp. 108124, 2003
Existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary
(
Citations: 20
)
M. M. Cavalcanti
,
V. N. Domingos Cavalcanti
,
M. L. Santos
Journal:
Applied Mathematics and Computation  AMC
, vol. 150, no. 2, pp. 439465, 2004
On a nonlinear wave equation associated with the boundary conditions involving convolution
(
Citations: 7
)
Le Thi Phuong Ngoc
,
Le Nguyen Kim Hang
,
Nguyen Thanh Long
Journal:
Nonlinear Analysistheory Methods & Applications  NONLINEAR ANALTHEOR METH APP
, vol. 70, no. 11, pp. 39433965, 2009