一类非线性阻尼Petrovsky方程整体解的能量衰减估计
Energy Decay Estimate of Global Solution for a Class of Nonlinear Damping Petrovsky Equations

作者: 陈 振 , 王 瑞 :河南农业大学信息与管理科学学院,郑州; 钞雅丽 :河南省体育运动学校,郑州;

关键词: 阻尼波方程初边值问题整体解能量衰减估计Damping Wave Equation Initial-Boundary Equation Global Solution Energy Decay Estimate

摘要:
本文主要研究非线性阻尼Petrovsky方程ua2u+a(1+|ut|r)ut=b|u|pu在有界区域的初边值问题。利用V. Komornik引理得到整体解的能量衰减估计。

Abstract: The nonlinear damping Petrovsky equation ua2u+a(1+|ut|r)ut=b|u|pu with initial-boundary conditions on bounded region is studied. The V. Komornik lemma here plays a crucial role in the energy decay estimate of global solution.

文章引用: 陈 振 , 王 瑞 , 钞雅丽 (2015) 一类非线性阻尼Petrovsky方程整体解的能量衰减估计。 理论数学, 5, 14-20. doi: 10.12677/PM.2015.51003

参考文献

[1] Komornik, V. (1994) Exact controllability and stabilization. The Multiplier Method, Masson, Paris.

[2] Payne, L.E. and Sattinger, D.H. (1975) Saddle points and instability of nonlinear hyperbolic equations. Israel Journal of Mathematics, 22, 273-303.

[3] Guesmia, A. (1998) Existence globale at stabilisation interne non lineaire d’un systeme de Petrovsky. Bulletin of the Belgian Ma-thematical Society—Simon Stevin, 5, 583-594.

[4] Guesmia, A. (1999) Energy decay for a damped nonlinear coupled system. Journal of Mathematical Analysis and Applications, 239, 38-48.

[5] Aassila, M. and Guesmia, A. (1999) Energy decay for a damped nonlinear hyperbolic equation. Applied Mathematics Letters, 12, 49-52.

[6] Benaissa, A. and Messaoudi, S.A. (2005) Exponential decay of solutions of a nonlinearly damped wave equation. Nonlinear Diffe-rential Equations and Applications, 12, 391-399.

[7] Georgiev, V. and Todorova, G. (1994) Existence of solutions of the wave equation with nonlinear damping and source terms. Journal of Differential Equations, 109, 295-308.

[8] Todorova, G. (1999) Stable and unstable sets for the Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms. Journal of Mathematical Analysis and Applications, 239, 213-226.

[9] Vitiliaro, E. (1999) Global nonexistence theorems for a class of evolution equations with dissipation. Archive for Rational Mechanics and Analysis, 149, 155-182.

[10] Liu, Y.C. and Zhao, J.S. (2006) On potential wells and applications to semilinear hyperbolic equations and parabolic equations. Nonlinear Analysis, 64, 2665-2687.

[11] Messaoudi, S.A. (2002) Global existence and nonexistence in a system of Petrovsky. Journal of Mathematical Analysis and Applications, 265, 296-308.

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