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

Long Nguyen Thanh (1) , Alain Pham Ngoc Dinh (2) , Le Xuan Truong (3)

1 Department of Mathematics and Computer Science
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 Department of Mathematics

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

Mots clés: Faedo-Galerkin method; global existence; contraction; nonlinear wave equation; viscoelastic; exponential decay

Domaines: Equations aux dérivées partielles [math.AP]

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. 2007. ⟨hal-00136410v1⟩