抽象Cauchy问题的适定性与算子半群  

THE WELLPOSEDNESS OF ABSTRACT CAUCHY PROBLEMAND SEMIGROUPS OF OPERATORS

作　　者：彭济根[1] 宋德功[1] 王绵森[1] 朱广田[2] 

机构地区：[1]西安交通大学数学系,西安710049 [2]中国科学院系统科学研究所,北京100080

出　　处：《系统科学与数学》1998年第2期225-229,共5页Journal of Systems Science and Mathematical Sciences

摘　　要：在算子A非稠定、问题解非指数有界的情况下，研究抽象Cauchy问题的适定性及其与A生成的算子族之间的关系．首先，引进（ACP1）的C适定性概念和C半群生成元的全新定义，证明：（ACP1）是C适定的充要条件是A生成C半群．并给出A生成非指数有界C半群的充分条件．另外，引进（ACP2）的（n，k）适定性定义，并讨论（n，k）适定性与积分余弦函数的关系．In the case where A is not defined densely and the solutions are exponentiallyunbounded, we consider the wellposedness of the abstract Cauchy Problem and its relation tothe semigroups generated by A. First, we introduce a new concept- C- wellposedness of (ACP1)and a new generator of C-sendgroups, and prove that (ACP1) is C-wellposed if and only if A isa generator of C-sendgroups; furthermore, we give a condition for A to generate a C-semingroupexponentially unbounded. Secondly, we introduce a new concept-the (n, k)-wellposedness of(ACP2), and prove that (ACP2) is (n＋1, n)-wellposed if and duly if A is a generator of 2ntimes integrated cosine function of operators.

关 键 词：抽象初值问题 适定性 生成元 C适定 算子半群 

分 类 号：O175.1[理学—数学] O152.7[理学—基础数学]