无界区域中的非线性双曲型方程
On Nonlinear Hyperbolic Equation in Unbounded Domain
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摘要: 本文研究无界区域中的非线性双曲方程utt+A2u+M(x,||A1/2u||22)Au=0这类问题的模型来自梁的横向挠曲方程.本文利用不动点方法结合能量估计证明了当M与x有关时,上述方程局部解的存在唯一性.Abstract: The following nonlinear hyperbolic equation is discussed in this paper:utt+A2u+M(x,||A1/2u||22)Au=0, where A=-Δ+I and x∈Rn. The model comes from the transverse deflection equation of an extensible beam. We prove that there exists a unique local solution of the above equation as M depends on x.
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[1] Woinowsky-Krieger, S., The effect of axial force on the vibration of hinged bars, J. Appl. Mech., 17 (1950), 35-36. [2] Medeiros, L. A., On a new class of nonlinear wave equation, J. Math. Appl., 69(1979),252-262. [3] Menzala, G. P., On global classical solutions of a nonlinear wave equation, J. Appl. Anal., 10 (1980), 179-195. [4] Biler, P., Remark on the decay for damped string and beam, Nonlinear Analysis, 10 (1986), 839-842. [5] Brito, E. H., Decay estimates for generalized damped extensible string and beam equation, Nonlinear Analysis, 8(1984),1489-1496. [6] Brito, E. H., Nonlinear initial-boundary value problems, Nonlinear Analysis, 11 (1987), 125-137. [7] Pereira, D. C., Exitence, uniqueness and asymptotic behavior for solutions of the nonlinear beam equation, Nonlinear Analysis, 14 (1990), 613-623. [8] Vasconcellos, C. F.,On a nonlinear wave equation in unbounded domains, Internat. J. Math. & Math. Sci., 11, 2 (1988), 335-342. [9] Goldstein, J., Time dependent hyperbolic equation, J. Func. Anal., 4 (1969), 31-49.
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