The Total Preservation of Unique Global Solvability of the First Kind Operator Equation With Additional Controlled Nonlinearity

被引：5
作者：
Chernov A.V. [1 ]
机构：
[1] Nizhni Novgorod State University named after N. I. Lobachevskii, pr. Gagarina 23, Nizhni Novgorod
来源：
Russian Mathematics | 2018年 / 62卷 / 11期
关键词：
controlled nonlinearity; evolutionary operator equation of the first kind in a Banach space; pseudoparabolic equation; system of Oskolkov equations; total preservation of unique global solvability;
D O I：
10.3103/S1066369X18110063
中图分类号：
学科分类号：
摘要：
For the Cauchy problem associated with an evolutionary operator equation of the first kind with an additional controlled term which nonlinearly depends on the phase variable, in a Banach space, we establish conditions for the total (on the set of admissible controls) preservation of unique global solvability under variation of the control parameter. We also establish the uniform bound for solutions. As examples, we consider initial-boundary value problems that are associated with a pseudoparabolic equation and a system of Oskolkov equations. © 2018, Allerton Press, Inc.
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页码：53 / 66
页数：13
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