Asymptotic behavior for a quasi-autonomous gradient system of expansive type governed by a quasiconvex function
| dc.contributor.author | Djafari Rouhani, Behzad | |
| dc.contributor.author | Rahimi Piranfar, Mohsen | |
| dc.date.accessioned | 2021-08-20T18:52:37Z | |
| dc.date.available | 2021-08-20T18:52:37Z | |
| dc.date.issued | 2021-03-18 | |
| dc.description.abstract | We consider the quasi-autonomous first-order gradient system u̇(t) = ∇φ(u(t)) + ƒ(t), t ∈ [0, +∞) u(0) = x0 ∈ H, where φ : H → ℝ is a differentiable quasiconvex function such that ∇φ is Lipschitz continuous. We study the asymptotic behavior of solutions to this system in continuous and discrete time. We show that each solution either approaches infinity in norm or converges weakly to a critical point of φ. This further concludes that the existence of bounded solutions and implies that φ has a nonempty set of critical points. Some strong convergence results, as well as numerical examples, are also given in both continuous and discrete cases. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 13 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Djafari Rouhani, B., & Rahimi Piranfar, M. (2021). Asymptotic behavior for a quasi-autonomous gradient system of expansive type governed by a quasiconvex function. <i>Electronic Journal of Differential Equations, 2021</i>(15), pp. 1-13. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14412 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, 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, 2021, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | First-order evolution equation | |
| dc.subject | Expansive type gradient system | |
| dc.subject | Asymptotic behavior | |
| dc.subject | Quasiconvex function | |
| dc.subject | Minimization | |
| dc.title | Asymptotic behavior for a quasi-autonomous gradient system of expansive type governed by a quasiconvex function | |
| dc.type | Article |