Regularization for evolution equations in Hilbert spaces involving monotone operators via the semi-flows method
| dc.contributor.author | Karakostas, George L. | |
| dc.contributor.author | Palaska, Konstantina | |
| dc.date.accessioned | 2021-08-18T14:18:56Z | |
| dc.date.available | 2021-08-18T14:18:56Z | |
| dc.date.issued | 2007-10-30 | |
| dc.description.abstract | In a Hilbert space H consider the equation d/dt x(t) + T(t)x(t) + α(t)x(t) = ƒ(t), t ≥ 0, where the family of operators T(t), t ≥ 0 converges in a certain sense to a monotone operator S, the function α vanishes at infinity and the function ƒ converges to a point h. In this paper we provide sufficient conditions that guarantee the fact that full limiting functions of any solution of the equation are points of the orthogonality set O(h; S) of S at h, namely the set of all x ∈ H such that ⟨Sx - h, x - z⟩ = 0, for all z ∈ S-1(h). If the set O(h; S) is a singleton, then the original solution converges to a solution of the algebraic equation Sz = h. Our problem is faced by using the semi-flow theory and it extends to various directions the works [1, 12]. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 18 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Karakostas, G. L., & Palaska, K. G. (2007). Regularization for evolution equations in Hilbert spaces involving monotone operators via the semi-flows method. <i>Electronic Journal of Differential Equations, 2007</i>(145), pp. 1-18. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14359 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Hilbert spaces | |
| dc.subject | Monotone operators | |
| dc.subject | Regularization | |
| dc.subject | Evolutions | |
| dc.subject | Semi-flows | |
| dc.subject | Limiting equations | |
| dc.subject | Full limiting functions | |
| dc.subject | Convergence | |
| dc.title | Regularization for evolution equations in Hilbert spaces involving monotone operators via the semi-flows method | |
| dc.type | Article |