Existence of solutions of the nonautonomous abstract Cauchy problem of second order

被引：6
|
作者：
Henriquez, Hernan R. [1 ]
机构：
[1] Univ Santiago, Dept Matemat, USACH, Santiago, Chile
来源：
SEMIGROUP FORUM | 2013年 / 87卷 / 02期
关键词：
Abstract Cauchy problem of second order; Mild solutions; Cosine functions of operators; Exponential vectors; FULLY DISCRETE APPROXIMATIONS; TIME-DEPENDENT PERTURBATION; HYPERBOLIC-EQUATIONS; EVOLUTION-EQUATIONS; HIGHER-ORDER; DIFFERENTIAL-EQUATIONS; BANACH-SPACES; PARABOLIC EQUATIONS; SOLUTION MAPPINGS; COEFFICIENTS;
D O I：
10.1007/s00233-013-9485-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper the existence of solutions of a nonautonomous abstract Cauchy problem of second order is considered. Assuming appropriate conditions on the operator of the equation, we establish the existence of mild solutions and, in some cases, we construct an evolution operator associated to the homogeneous equation. Using this evolution operator we obtain existence of solutions for the inhomogeneous equation. Finally, we apply our results to study the existence of solutions of the nonautonomous wave equation.
引用
收藏
页码：277 / 297
页数：21
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