Stabilization and control of subcritical semilinear wave equation in bounded domain with Cauchy-Ventcel boundary conditions

作     者：A.Kanoune N.Mehidi 

作者机构：Laboratory of Applied MathematicsDepartment of MathematicsUniversity of Bejaia06000 BejaiaAlgeria 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2008年第29卷第6期

页      面：787-800页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

主　　题：stabilization exact controllability limit problems semilinear subcritical,partial differential equations Cauchy-Ventcel 

摘      要：We analyze the exponential decay property of solutions of the semilinear wave equation in bounded domain Ω of R^N with a damping term which is effective on the exterior of a ball and boundary conditions of the Cauchy-Ventcel type. Under suitable and natural assumptions on the nonlinearity, we prove that the exponential decay holds locally uniformly for finite energy solutions provided the nonlinearity is subcritical at infinity. Subcriticality means, roughly speaking, that the nonlinearity grows at infinity at most as a power p 〈 5. The results obtained in R^3 and RN by B. Dehman, G. Lebeau and E. Zuazua on the inequalities of the classical energy （which estimate the total energy of solutions in terms of the energy localized in the exterior of a ball） and on Strichartz＇s estimates, allow us to give an application to the stabilization controllability of the semilinear wave equation in a bounded domain of R^N with a subcritical nonlinearity on the domain and its boundary, and conditions on the boundary of Cauchy-Ventcel type.