非线性弹性杆振动方程解的渐近行为.pdf

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6、H0=L2()L2();H1=H01()H01();H2=D(A)D(A):.·‚©Oy²¯K(P)3H1þ•êáÚf•359(H1;H2)•êáÚf•35.'''………ccc:š‚55Ä•§;ÛáÚf;•êáÚf;©/‘ꥥ¥ããã©©©aaaÒÒÒ:O175.15iiAbstractInthismasterdissertation,Weprovetheexistenceofglobalattractorsandexponentialattractorsofnonlinearelasticrodoscillationequation.T

7、hemainworksare:1.wearedevotedtostudyingtheexistenceofglobalattractorofH01()H01()and(H1;H2)-globalattractorrespectivelythefollowingequation:u+tt4u4ut!4utt+f(u)=g(x);(x;t)2R;ujt=0=u0;utjt=0=u1;8x2;uj@=0;8t0;Furthermore,weobtainedthatglobalattractorA0ofnonlinearelasticrodoscillati

8、onequation(P)hasnitefractaldimensionandprovedattractorA0isthebounedsubsetsinH2=D(A)D(A)withtheskillsofdecompositionforsemigroup,whereH0=L2()L2();H1=H01()H01();H2=D(A)D(A)2.weprovetheexistenceofexponentialattractorofH1and(H1;H2)exponentialattractorofnonlinearelasticrodoscillatio

9、nequation(P)