Regularity and Rothe method error estimates for parabolic hemivariational inequality

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:389

Article

Kalita, Piotr

关键词: Hemivariational inequality;    Differential inclusion;    Clarke subdifferential;    Parabolic problem;    Rothe method;    Regularity;    Error estimates;   

DOI  :  10.1016/j.jmaa.2011.12.007

来源: Elsevier

【 摘 要 】

This paper deals with regularity of solutions to the abstract operator version of parabolic partial differential inclusion of the form u'(t) + Au(t) + iota*delta J(iota u(t)) (sic) f(t) with the multivalued term given in the form of Clarke subdifferential of a locally Lipschitz functional J. Using the Rothe method, it is shown that under appropriate assumptions on the data, the solution has the increased regularity. Three regularity theorems are given. The first one concerns the regularity of solution in the Besov space B-2 infinity(1/2)(0, T; H). The second theorem provides assumption under which the solution lies in the space H-1(0, T; H) boolean AND L-infinity(0, T; V) boolean AND C([0, T]; V-weak). The last one shows that if the operator A is strongly monotone and the multivalued term satisfies the relaxed monotonicity assumption then the unique solution also belongs to H-1(0, T; V) boolean AND W-1,W-infinity(0, T; H). In the last case the error estimates on the Rothe method are also proved. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free