Hilbert空间弱阻尼波方程周期解的存在唯一性OA
Existence and uniqueness of periodic solutions for weakly damped wave equations in Hilbert spaces
讨论Hilbert空间H中弱阻尼波方程u″(t)+2cu'(t)+Au(t)=f(t,u(t)),t∈R周期解的存在唯一性,其中A:D(A)⊂H →H为正定自伴算子,且有紧预解式,f:R×H →H连续,f(t,x)关于t以ω为周期,c>0为阻尼系数.在小阻尼系数0<c<1情形,应用算子半群理论与不动点定理获得了方程ω-周期解的存在唯一性.
The existence and uniqueness of periodic solutions for weakly damped wave equation u″(t)+2cu'(t)+Au(t)=f(t,u(t)),t∈R are discussed in a Hilbert space H,where A:D(A)⊂H →H is a positive definite self-adjoint operator with a compact resolvent in H,f:R×H →H is continuous,f(t,x)is ω-periodic in t,and c>0 is the damping coefficient.By applying the semigroup theory of linear operators and fixed-point theorem,the existence and uniqueness of ω-periodic solution of the equations are obtained.
高芸;李永祥
西北师范大学 数学与统计学院,甘肃 兰州 730070西北师范大学 数学与统计学院,甘肃 兰州 730070
数理科学
Hilbert空间弱阻尼波方程阻尼系数周期解算子半群存在唯一性
Hilbert spaceweakly damped wave equationdamping coefficientperiodic solutionoperator semigroupexistence and uniqueness
《西北师范大学学报（自然科学版）》 2026 (1)
72-76,92,6
国家自然科学基金资助项目(12061062)
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