Compact families of piecewise constant functions in Lp(0, T; B)

被引：81

作者：

Dreher, Michael ^{[2
]}

Juengel, Ansgar ^{[1
]}

机构：

[1] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria

[2] Univ Konstanz, Fachbereich Math & Stat, D-78457 Constance, Germany

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 06期

基金：

奥地利科学基金会;

关键词：

Compactness; Aubin lemma; Rothe method;

D O I：

10.1016/j.na.2011.12.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A strong compactness result in the spirit of the Lions-Aubin-Simon lemma is proven for piecewise constant functions in time (u(tau)) with values in a Banach space. The main feature of our result is that it is sufficient to verify one uniform estimate for the time shifts u(tau) - u(tau) (center dot - tau) instead of all time shifts u(tau) - u(tau) (center dot - h) for h > 0, as required in Simon's compactness theorem. This simplifies significantly the application of the Rothe method in the existence analysis of parabolic problems. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：3072 / 3077

页数：6

共 8 条

[1]

Amann H., 2000, Glas. Mat. Ser., V35, P161

[2]

Andreianov B., 2011, TIME COMPACTNESS TOO

[3] Doubly nonlinear evolution equations of second order: Existence and fully discrete approximation [J].

Emmrich, Etienne ;

Thalhammer, Mechthild .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 251 (01) :82-118

[4]

Gallouet T., 2012, COMMUN PURE IN PRESS

[5]

Kacur J., 1985, TEUBNER TEXTE MATH, V80

[6]

Roubicek T., 2005, NONLINEAR PARTIAL DI

[7] COMPACT-SETS IN THE SPACE LP(O, T-B) [J].

SIMON, J .

ANNALI DI MATEMATICA PURA ED APPLICATA, 1986, 146 :65-96

[8] COMPACTNESS PROPERTIES OF THE DG AND CG TIME STEPPING SCHEMES FOR PARABOLIC EQUATIONS [J].

Walkington, Noel J. .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 47 (06) :4680-4710

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