摘要
在Ω×(0,∞)上考虑一类非齐次粘弹性变密度方程|u_(t)|^(ρ)u_(tt)+Δ^(2)u-M∫_(Ω)|▽u|^(2)d xΔu-μΔu tt-∫^(t)0g(t-s)Δ^(2)u(s)d s=f(u).在记忆核和源项的一般假设下,通过建立微分不等式,证明了其初边值问题解的能量衰减率.
A class of inhomogeneous viscoelastic variable density equations is considered in this paper|u_(t)|^(ρ)u_(tt)+Δ^(2)u-M∫_(Ω)|▽u|^(2)d xΔu-μΔu tt-∫^(t)0g(t-s)Δ^(2)u(s)d s=f(u).inΩ×(0,∞).Under the general assumption of memory kernel and source term,the energy decay rate of the initial boundary value problem is proved by establishing the differential inequality.
作者
孔令硕
李傅山
KONG Lingshuo;LI Fushan(School of Mathematical Sciences,Qufu Normal University,273165,Qufu,Shandong,PRC)
出处
《曲阜师范大学学报（自然科学版）》
CAS
2023年第2期51-61,共11页
Journal of Qufu Normal University(Natural Science)
基金
山东省自然科学基金(ZR2019MA067).
关键词
记忆核
变密度
粘弹性方程
能量衰减
memory kernel
variable density
viscoelastic equation
energy decay
