Nonresonance and global existence of nonlinear elastic wave equations with external forces

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• 作者：Yi Zhou (1) yizhou@fudan.ac.cn
  Wei Xu (1) xuwei-partial@hotmail.com
• 关键词：Nonlinear elasticity – ; Global existence – ; Null condition – ; External force
• 刊名：Chinese Annals of Mathematics - Series B
• 出版年：2012
• 出版时间：May 2012
• 年：2012
• 卷：33
• 期：3
• 页码：437-452
• 全文大小：217.3 KB
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  8. Tahvildar-Zadeh, A. S., Relativistic and nonrelativistic elastodynamics with small shear strains, Ann. Inst. H. Poincar茅-Phys. Th茅or., 69, 1998, 275–307.
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• 作者单位：1. School of Mathematical Sciences, Fudan University, Shanghai, 200433 China
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Applications of Mathematics
  Chinese Library of Science
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1860-6261

文摘

This paper establishes the global existence of classical solution to the system of homogeneous, isotropic hyperelasticity with time-independent external force, provided that the nonlinear term obeys a type of null condition. The authors first prove the existence and uniqueness of the stationary solution. Then they show that the solution to the dynamical system converges to the stationary solution as time goes to infinity.