Well-posedness of linear singular evolution equations in Banach spaces: theoretical results

被引:0
|
作者
Bortolan, M. C. [1 ]
Brito, M. C. A. [1 ]
Dantas, F. [2 ]
机构
[1] Univ Fed Santa Catarina UFSC, Ctr Ciencias Fis & Matemat, Dept Matemat, Campus Florianopolis, BR-88040090 Florianopolis, SC, Brazil
[2] Univ Fed Sergipe, Dept Matemat, Sao Cristovao, SE, Brazil
关键词
singular problem; degenerated problem; well-posedness; generalized semigroup; generator;
D O I
10.1007/s10476-025-00067-8
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this work we deal with a singular evolution equation of the form {E-u(center dot)= Au,t>0,<br /> u(0) = u0, where both A and E are linear operators, with E bounded but not necessarily injective, defined in adequate subspaces of a given Banach space X. By using the concept of generalized semigroups, our goal is to prove a Hille-Yosida type theorem for this problem, that is, to find necessary and sufficient conditions under which A is the generator of a generalized semigroup {U(t):t >= 0}. This problem is dealt with by making use of the E-spectral theory and the concept of generalized integrable families. Finally, we present an abstract example that illustrates the theory.
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页码:99 / 128
页数:30
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