Acta mathematica scientia,Series A ›› 2003, Vol. 23 ›› Issue (6): 704-710.
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ZHANG Quan-Ju
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陕西省教育厅专项基金资助（01JK201）项目
Abstract:
This paper deals with the hyperbolic equation in the form of utt+A2u+M(x，‖A1/2u‖22)Au=0，which comes from the mathematical description of the tension of a extensible bea m, and the existence and uniqueness of Cauchy problems for this equation are pre sented here. An existence and uniqueness theorem of local solvability is proven for this equation, and compared with the existing results, the author's conditio ns restri cted to the nonlinear term of this equation are much general. In fact, the resul ts given here are obtained by breaking all the former restrictions on the nonlin ear term.
Key words: Tension of a extensible beam, Hyperbolic equation, Cauchy problems, Existence and uniqueness theorem
CLC Number:
ZHANG Quan-Ju. The Cauchy Problems of a class of Equations |for the Tension of Extensible Beam[J].Acta mathematica scientia,Series A, 2003, 23(6): 704-710.
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[1]Woinowsky K，Krieger S. The effect of axial force on the vibration of hin ged bars. J Appl Mech，1950，17：35-36 [2]Medeiros L A. On a new class of nonlinear wave equation. J Math Appl，19 79，69：252-262 [3]Biller P. Remark on the decay for damped strint and beam. Nonlinear Analysis，1986，10：839-842 [4]Brito E H. Decay estimates for generalized damped extensible string and b eam equation. Nonlinear Analysis，1984，8：1489-1496 [5]Brito E H. Nonlinear initialboundary value problems. Nonlinear Anal ysis，1987，11：125-137 [6]Goldstein J. Time dependent hyperbolic equation. J Func Anal，196 9，2：31-49 [7]Ball J M. Initialboudary value problems for an extensive beam. J Math Appl Analysis，1973，42：81-90 [8]Menzala G P. On global classical solutions of a nonlinear wave equations . J Math Applic，1980，10：178-195 [9]Pereira D C. Existence，uniqueness and asymptotic behavior for solutions of the nonlinear beam equation. Nonlinear Analysis，1990，14:613 -623 [10]Ball J M. Stability theory for an extensible beam. J Differ Equns，197 3，14：399-418 [11]Dickey R W. Free vibrations and dynamic buckling of extensive beam. J Math Anal Appl，1970，29：443-454 [12]Burgreen D. Free vibrations of a pinended column with constant distanc e between pin ends. J Appl Mech，1951，18：135-139
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