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影响因子：1.1

DOI码：10.1515/jiip-2017-0082

发表刊物：Journal of Inverse and Ill-Posed Problems

关键字：Cahn-Hilliard equation; backward problem; Carleman estimate; conditional stability

摘要：We consider a Cahn-Hilliard equation in a bounded domain Omega in R-n over a time interval (0, T) and discuss the backward problem in time of determining intermediate data u(x, theta), theta epsilon (0, T), x epsilon Omega from the measurement of the final data u(x, T), x epsilon Omega. Under suitable a priori boundness assumptions on the solutions u(x, t), we prove a conditional stability estimate for the semilinear Cahn-Hilliard equation parallel to u(., theta)parallel to(L2(Omega)) <= C parallel to u(., T)parallel to(kappa 0)(H2(Omega)), and a conditional stability estimate for the linear Cahn-Hilliard equation parallel to u(., theta)parallel to(H beta(Omega)) <= C parallel to u(. , T)parallel to(kappa 1)(H2(Omega)), where theta epsilon (0, T), beta epsilon (0, 4) and kappa(0), kappa(1) epsilon (0, 1). The proof is based on a Carleman estimate with the weight function e(2se lambda t) with large parameters s, lambda epsilon R^+.

合写作者：李书敏

第一作者：尚云侠

论文类型：期刊论文

论文编号：000635601700001

学科门类：理学

文献类型：J

卷号：29

期号：2

页面范围：159-171

ISSN号：0928-0219

是否译文：否

发表时间：2021-04-01

收录刊物：SCI、EI

发布期刊链接：https://www.degruyter.com/document/doi/10.1515/jiip-2017-0082/html