Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type

Le Xuan Truong (1) , Le Thi Phuong Ngoc (2) , Alain Pham Ngoc Dinh (3) , Nguyen Thanh Long (4)

1 Department of Mathematics
2 Mathematics department
3 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
4 UNS-HCMC - University of Natural Science, Vietnam National University HoChiMinhCity

This paper is devoted to study a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under suitable conditions, we prove that any weak solutions with negative initial energy will blow up in finite time. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results

Mots clés: Nonlinear wave equation; Local existence; Global existence; Blow up; Exponential decay

Domaines: Equations aux dérivées partielles [math.AP]

Le Xuan Truong, Le Thi Phuong Ngoc, Alain Pham Ngoc Dinh, Nguyen Thanh Long. Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type. 2011. ⟨hal-00585439v2⟩