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Dynamic boundary systems with boundary feedback and population system with unbounded birth process
Author(s) -
Mei ZhanDong,
Peng JiGen
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3175
Subject(s) - semigroup , mathematics , boundary (topology) , dynamical systems theory , class (philosophy) , population , process (computing) , boundary value problem , population model , mathematical analysis , computer science , physics , operating system , demography , quantum mechanics , artificial intelligence , sociology
This paper is concerned with a class of dynamic boundary systems with boundary feedback. The well‐posedness of the considered systems is proved under some regularity conditions. Moreover, some spectral properties are derived. As an application, the well‐posedness and the asymptotic behavior of population dynamical systems with unbounded birth process ‘ B ( t ) = ∫ 0 ∞ β ( a ) u ( t − τ , a ) da , t ≥ 0 ’ are solved. Such population dynamical systems were pointed out in [S. Piazzera, Math. Methods Appl. Sci., 27 (2004), 427‐439] to be a current research topic in semigroup theory and still an open problem. Copyright © 2014 John Wiley & Sons, Ltd.