Skip to Main content Skip to Navigation
Journal articles

EXISTENCE AND DECAY OF SOLUTIONS OF A NONLINEAR VISCOELASTIC PROBLEM WITH A MIXED NONHOMOGENEOUS CONDITION

Abstract : 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)=û_{0}(x), u_{t}(x,0)={û}_{1}(x), where \eta \geq 0, q\geq 2 are given constants {û}_{0}, {û}_{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.
Complete list of metadatas

Cited literature [9 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00136410
Contributor : Alain Pham Ngoc Dinh <>
Submitted on : Sunday, May 27, 2007 - 4:48:11 PM
Last modification on : Monday, May 4, 2020 - 2:18:13 PM
Document(s) archivé(s) le : Thursday, September 23, 2010 - 4:23:03 PM

Files

LATruong.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00136410, version 3
  • ARXIV : 0705.3959

Collections

Citation

Long Nguyen Thanh, Alain Pham Ngoc Dinh, Le Xuan Truong. EXISTENCE AND DECAY OF SOLUTIONS OF A NONLINEAR VISCOELASTIC PROBLEM WITH A MIXED NONHOMOGENEOUS CONDITION. Numerical Functional Analysis and Optimization, Taylor & Francis, 2008, 29 (11-12), pp.1363-1393. ⟨hal-00136410v3⟩

Share

Metrics

Record views

306

Files downloads

232