Long-time behavior of a model of extensible beams with nonlinear boundary dissipations

Author(s)

Ma, T. F. ^[1] ; Narciso, V. ^[2] ; Pelicer, M. L. ^[3]

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Estadual Mato Grosso do Sul, Unidade Dourados, Nucleo Ciencias Exatas, BR-79804970 Dourados, MS - Brazil

^[3] Univ Estadual Maringa, Dept Ciencias, BR-87360000 Goioere, PR - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 396, n. 2, p. 694-703, DEC 15 2012.
• Web of Science Citations: 13

Abstract

This paper is concerned with the long-time behavior of a model of extensible beams u(tt) + u(xxxx) - M (integral(L)(0) vertical bar u(x)vertical bar(2) dx) u(xx) = h, defined in a bounded interval (0, L), where M is a continuous nonnegative function and h is a static load. To this problem little is known with nonlinear boundary conditions. One considers the case where a nonlinear forcing interacts with the shear force at the boundary. Then the existence of a global attractor is proved with a sole boundary damping. (C) 2012 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 10/12202-9 - Asymptotic stability of nonlinear hyperbolic equations
• Grantee: Ma To Fu
• Support Opportunities: Regular Research Grants