期刊论文详细信息
JOURNAL OF DIFFERENTIAL EQUATIONS 卷:249
Non-uniform dependence and well-posedness for the hyperelastic rod equation
Article
Karapetyan, David
关键词: Hyperelastic rod equation;    Periodic;    Non-periodic;    Initial value problem;    Sobolev spaces;    Well-posedness;    Continuity of solution map;    Non-uniform dependence;    Approximate solutions;    Energy estimates;   
DOI  :  10.1016/j.jde.2010.04.002
来源: Elsevier
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【 摘 要 】

It is shown that the solution map for the hyperelastic rod equation is not uniformly continuous on bounded sets of Sobolev spaces with exponent greater than 3/2 in the periodic case and greater than 1 in the non-periodic case. The proof is based on the method of approximate solutions and well-posedness estimates for the solution and its lifespan. (C) 2010 Elsevier Inc. All rights reserved.

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