Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary. (16th October 2005)

• Record Type: Journal Article
• Authors: Santos, M. L.; Ferreira, J.; Raposo, C. A.
• Is Part Of: Abstract and applied analysis. Volume 2005:Number 8(2005)
• Page Start: 901
• Page End: 919
• Publication Date: 2005-10-16
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/AAA.2005.901
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We prove the exponential decay in the casen > 2, as time goes to infinity, of regular solutions for the nonlinear beam equation with memory and weak dampingu t t + Δ 2 u − M ( ‖ ∇ u ‖ L 2 ( Ω t ) 2 ) Δ u + ∫ 0 t g ( t − s ) Δ u ( s ) d s + α u t = 0 in Q ^ in a noncylindrical domain ofℝ n + 1 ( n ≥ 1 ) under suitable hypothesis on the scalar functionsM andg, and whereα is a positive constant. We establish existence and uniqueness of regular solutions for anyn ≥ 1 .