Global well-posedness and stability of semilinear Mindlin-Timoshenko system

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:418

Article

Pei, Pei¹  Rammaha, Mohammad A.¹  Toundykov, Daniel¹ 

[1] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

关键词: Plate;    Mindlin-Timoshenko;    Reissner-Mindlin;    Damping;    Source;    Potential well;    Global existence;    Stability;    Decay rates;    Blow-up;   

DOI  :  10.1016/j.jmaa.2014.03.014

来源: Elsevier

【 摘 要 】

We study long-term behavior of Reissner-Mindlin-Timoshenko (RMT) plate systems, focusing on the interplay between nonlinear viscous damping and source terms. The sources may represent restoring forces, but may also be focusing thus potentially amplifying the total energy which is the primary scenario of interest. This work complements [28] which established local well-posedness of this problem, global well-posedness when damping dominates the sources (in an appropriate sense) and a blow-up in the complementary scenario assuming negative total initial energy. The current paper develops the potential well theory for the RMT system: it proves global existence for potential well solutions without restricting the source exponents, derives explicit energy decay rates dependent on the order of the damping exponents, and verifies a blow-up result for positive total initial energy. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free