不完全二階柯西問題的l39;p最大正則性

1、華中科技大學(xué)碩士學(xué)位論文不完全二階柯西問題的L-最大正則性姓名：馮燕申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：黃永忠20070528AbstractEstablishing Lp-maximal regularity for large classes of classical partial differen-tial operators and systems does help to study regularity of the

2、ir solutions and exis-tence of nonlinear equations. In fact, frequently a partial differential equation can betransformed into an ordinary differential equation with values in an infinite dimen-sional space. Cauchy probl

3、em is cauchy style of partial differential equations. Forthese reasons much attendtion have been paid to Lp-maximal regularity of one orderCauchy problem since sixties of last century. In the ninties good results have be

4、enobtained. This paper is to study Lp-maximal regularity for imcomplete second orderCauchy problems, furthermore results from various sides have been obtained. Twocriteria—multipler and functional calculus of Lp-maximal

5、regularity are obtained, andthe analyticity of the corresponding sine operator is considered. On the other hand,we introduce the connection of Lp-maximal regularity among imcomplete second orderCauchy problems, periodic

6、problems, the corresponding one order Cauchy problems.In this paper we use multiplier characterization and operator-sum method, that isto say, L.Weis’ operator-valued multiplier theorem, operator-sum theorem and operator

7、-valued Marcinkiewicz multiplier theorem. Meanwhile, we use many methods, tech-niques and results from the functional analysis including semigroup of operators, func-tional calculs, operator-sum theorem, embeded theorem,

8、 UMD-space and so on. Weuse some results and means of one order Cauchy problem to obtain systematic resultson Lp-maximal regularity of imcomplete second order Cauchy problems.The significance of this paper is not only to

9、 perfect the system on Lp-maximalregularity of imcomplete second order Cauchy problems, but also set a foundation forthe posedness of quasilinear evolution equations and non-automous systems.Key words: Imcomplete second