指数有界双连续n阶α次积分C半群与高阶抽象Cauchy问题研究  

Study on Exponential Bounded Bicontinuous N-order Alpha-integral C Semigroups and Higher Order Abstract Cauchy Problem

作　　者：葛国菊[1] GE Guoju(School of Mathematics and Big Data,Chaohu University,Hefei 238024,China)

机构地区：[1]巢湖学院数学与大数据学院,安徽合肥238024

出　　处：《佳木斯大学学报（自然科学版）》2024年第4期173-176,92,共5页Journal of Jiamusi University：Natural Science Edition

摘　　要：算子半群理论在求解Cauchy问题等领域具有很大的应用价值,并且其在泛函分析理论等各方面的研究中同样有着重要意义。此次研究在Banach空间上,基于泛函分析、算子半群理论对柯西问题进行探讨。并基于n阶α次积分C半群的生成定理,对指数有界双连续n阶α次积分C半群的生成定理与其Laplace逆变换表达式进行推算。由结果可知,L∞范数误差在分数阶n为1.47时达到最低值,为0.04,这表明其与实际值极为接近。在T=0.2,0.5两种时刻下,中精确解和正则解的变化趋势基本一致,并且二者的误差在x∈0.1,0.9区间内接近于0。研究有效验证了指数有界双连续n阶α次积分C半群解决高阶抽象Cauchy问题具有适用性与可靠性。Operator semigroup theory has great application value in solving Cauchy problem and it is also of great significance in functional analysis theory and other aspects of research.Based on functional analysis and operator semigroup theory,this study explores Cauchy problem in Banach space.Based on the formation theorem of order integral semigroups,the formation theorem of exponential bounded bicontinuous order integral semigroups and its Laplace inverse transformation expression are calculated.It can be seen from the results that the norm error reaches the lowest value,0.04,when the fractional order is 1.47,indicating that it is very close to the actual value.At the time of T=0.2,0.5,the variation trend of the medium exact solution and the regular solution is basically the same,and the errors of both are close to 0 within the interval x∈0.1,0.9.The applicability and reliability of solving high order abstract Cauchy problem with exponential bounded bicontinuous order integral semigroups are validated.

关 键 词：高阶抽象Cauchy问题 适定性 指数有界 双连续 n阶α次积分C半群 

分 类 号：O177.2[理学—数学]