THE REGULARITY AND EXPONENTIAL DECAY OF SOLUTION FOR A LINEAR WAVE EQUATION ASSOCIATED WITH TWO-POINT BOUNDARY CONDITIONS

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 concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this problem by the construction of a suitable Lyapunov functional.

Mots clés: Faedo-Galerkin method; Global existence; nonlinear wave equation; two-point boundary conditions

Domaines: Equations aux dérivées partielles [math.AP]

Le Xuan Truong, Le Thi Phuong Ngoc, Alain Pham Ngoc Dinh, Nguyen Thanh Long. THE REGULARITY AND EXPONENTIAL DECAY OF SOLUTION FOR A LINEAR WAVE EQUATION ASSOCIATED WITH TWO-POINT BOUNDARY CONDITIONS. Nonlinear Analysis: Real World Applications, 2010, 12 (3), pp.1289-1303. ⟨hal-00294600v2⟩