一類半線性拋物系統(tǒng)的局部零能控性.pdf

1、華中師范大學(xué)碩士學(xué)位論文一類半線性拋物系統(tǒng)的局部零能控性姓名：梁勇申請學(xué)位級別：碩士專業(yè)：運(yùn)籌學(xué)與控制論指導(dǎo)教師：汪更生20040501ABSTRACTThispaperconcernsthelocalnullcontrollabilityforthefollowingsystem(。，t)∈Q(o，t)∈Q(X，t)∈∑z∈Q(I)whereQC即(禮∈1，2，3))isaboundednonemptyopensetwithasmoo

2、thboundary砌，Q=QX(0，T)，∑=aQX(0，T)，m(衛(wèi))isthecharacteristicfunctionofthesubsetuCQ，灶，口arethecontrolfunctionsactinginuX【0，T]HereT0，。，6，c，a，5，8areconstantsThelocalnullcontrollabilityproblemfor(I)canbeformulatedasfollows：GivenT

3、0，(Yo，ZO)∈L2(n)XL2(Q)，inaneighbourhoodof(0，o)，tofindcontrols讓and“∈L2∞(o，T))suchthatthesolution(Y，。)to(I)satisfiesy(T)=0，z(T)=0ThispaperismadeuDofthreeparts，Partoneintroducesthebackgroundofthesystemandtherevelantresearchp

4、rogressFurthermore，westateourmainresultsfollowingfromsomeretropectionoftheresultsobtainedbypreviousmathematicians，iethelocalnullcontrollabilityfor(I)holdsundersomeassumptionsontheinitialdatayoandZ0：ParttwofirstlyUnearize

5、sthesystem(I)，thenintroducessomeknownresults，mainlytheCarlemaninequalityforlinearparabolicsystem(Lemma22)，whichwillbeusedinthefollowingtextByapplyingthislemma，weobtainthetheCarlemaninequalityforthelinearizedsystem(Lemma2

6、4)，fromwhichweprovethenullcontroUabifityforthelinearizedsystem(Theorem231Partthreeprovesthelocalnullcontrollabilityfor(I)，ie，Theorem33，byapplyingKakutanifixedpointtheorem1l㈦池ZZ=彬酗吼歸““=棚22曲，仕驢咎矗Ⅵ的如矗o?！鲆?、機(jī)yZa一巍0葉計(jì)鼢慨Il叫m一歸刊