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 | |
【 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.
【 授权许可】
Free
【 预 览 】
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10_1016_j_jde_2010_04_002.pdf | 329KB | download |