Dynamic Analysis of a Nonlinear Timoshenko Equation

Abstract and Applied Analysis - Tập 2011 Số 1 - 2011
Jorge A. Esquivel‐Avila1
1Análisis y análisis funcional (SNI 2)

Tóm tắt

We characterize the global and nonglobal solutions of the Timoshenko equation in a bounded domain. We consider nonlinear dissipation and a nonlinear source term. We prove blowup of solutions as well as convergence to the zero and nonzero equilibria, and we give rates of decay to the zero equilibrium. In particular, we prove instability of the ground state. We show existence of global solutions without a uniform bound in time for the equation with nonlinear damping. We define and use a potential well and positive invariant sets.

Từ khóa


Tài liệu tham khảo

10.1016/0022‐247X(73)90121‐2

10.1016/0022‐0396(73)90056‐9

10.1007/BF00282203

Hale J. K., 1988, Asymptotic Behavior of Dissipative Systems

Haraux A., 1987, Semilinear Hyperboloic Problems in Bounded Domains

10.1007/BF02761595

10.1006/jdeq.1994.1051

10.1016/0362‐546X(95)00119‐G

10.1007/s00526‐008‐0188‐z

10.1512/iumj.2007.56.2990

10.1006/jmaa.1998.6057

10.3934/dcds.2002.8.675

10.1016/j.jmaa.2003.10.020

10.1016/j.jde.2004.04.011

10.1142/S0219199704001483

10.1016/j.jde.2007.02.004

10.5269/bspm.v25i1‐2.7427

10.1016/j.na.2009.11.013

10.1016/j.jmaa.2004.08.039

10.1016/S0022‐0396(02)00023‐2

10.1023/A:1022945512181

Esquivel-Avila J. A., 2003, Dynamic systems and Applications, 198

10.1016/S0362‐546X(02)00155‐4

10.1016/S0022‐247X(02)00701‐1

10.3934/dcds.2004.10.787

10.1016/0022‐0396(78)90032‐3

Brézis H., 1983, Analyse Fonctionnelle, Théorie et Applications

Thông tin
Thông tin xuất bản

Abstract and Applied Analysis

Tập 2011 Số 1

Thông tin tác giả