Mathematics – Analysis of PDEs
Scientific paper
2007-05-27
Numerical Functional Analysis and Optimization / Numerical Functional Analysis and Optimization An International Journal 29, 1
Mathematics
Analysis of PDEs
26 pages
Scientific paper
We study the initial-boundary value problem for a nonlinear wave equation given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u) , 0 < x < 1, 0 < t < T, u_{x}(0,t)=u(0,t), u_{x}(1,t)+\eta u(1,t)=g(t), u(x,0)=\^u_{0}(x), u_{t}(x,0)={\^u}_{1}(x), where \eta \geq 0, q\geq 2 are given constants {\^u}_{0}, {\^u}_{1}, g, k, f are given functions. In part I under a certain local Lipschitzian condition on f, a global existence and uniqueness theorem is proved. The proof is based on the paper [10] associated to a contraction mapping theorem and standard arguments of density. In Part} 2, under more restrictive conditions it is proved that the solution u(t) and its derivative u_{x}(t) decay exponentially to 0 as t tends to infinity.
Ngoc Dinh Alain Pham
Thanh Long Nguyen
Truong Le Xuan
No associations
LandOfFree
Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-99244