Academic Journal
The topological structure of solution sets and approximate controllability for semilinear evolution problems with non-compact semigroups.
| Τίτλος: | The topological structure of solution sets and approximate controllability for semilinear evolution problems with non-compact semigroups. |
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| Συγγραφείς: | Liang, Yixing1 (AUTHOR), Fan, Zhenbin2 (AUTHOR) zbfan@yzu.edu.cn, Li, Gang2 (AUTHOR) |
| Πηγή: | International Journal of Control. Aug2026, Vol. 99 Issue 8, p2477-2497. 21p. |
| Θεματικοί όροι: | *Nonlinear evolution equations, *Controllability in systems engineering, *Topology, *Linear operators, *Fixed point theory |
| Περίληψη: | This work is concerned with the topological structure of solution sets and the approximate controllability for integer-order semilinear evolution problems with non-compact semigroups. To overcome the difficulty of lacking compactness, we prove the existence of a specific continuous linear mapping and construct several estimations of non-compact measures in $ L^{2}([0,T];V) $ L 2 ([ 0 , T ] ; V). Then, the main results of this paper are derived by means of some standard fixed point theorem methods. Finally, we present an example to demonstrate the applicability of our theoretical results. To the best of our knowledge, this paper is among the few works that study the topological structure of solution sets together with approximate controllability for semilinear evolution problems in a non-compact semigroup framework under the assumptions adopted herein. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
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