具有记忆项的kirchhoff型梁方程整体解的存在性和衰减性  

Global Existence and Uniform Decay of Solutions to the Kirchhoff Type Beam Equations with Memory

作　　者：韩英豪[1] 周靖楠[1] 张艳桃[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《吉林师范大学学报（自然科学版）》2010年第2期5-10,共6页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(10471018)

摘　　要：设Ω是具有光滑边界的Rn的有界开区域,H=L2(Ω).在空间H上考虑了具有记忆项的非退化kirch-hoff型梁方程.utt+A2u+(a+M(‖A1/2u‖2))Au-∫0tg(t-τ)Au(τ)dτ+but=f(u).其中A是H上的一个线性算子,M和g是实函数.针对方程的初始能量非负且充分小的情况证明了整体弱解的存在性和唯一性.我们还研究了解的渐近行为,在衰减项和记忆项满足适当的条件下证明了解的指数衰减性.Let Ω be a bounded open domain in Rn with smooth boundary,H=L2（Ω）.We consider non-degenerate Kirchhoff type beam equations with memory term on the Hilbert space H utt＋A^2u＋（a＋M（‖A1/2u‖^2））Au-∫0^tg（t-τ）Au（τ）dτ＋but=f（u）. Where A is a linear operator in H,M and g are real functions.When the initial energy associated with the equations is non-negative and small,we prove the global existence and uniqueness of the weak solutions.We also study the asymptotic behaviour of the solutions.Under suitable assumptions on the damping term and memory term we prove the exponential decay of the solutions.

关 键 词：kirchhoff型梁方程 记忆项 整体解 指数衰减性 

分 类 号：O175.29[理学—数学]