Tạp chí Khoa học, S. 5(70) (2015)

Cỡ chữ:  Nhỏ  Vừa  Lớn

A long time behavior for gradient-like systems under a weak angle condition

Tran Minh Phuong, Nguyen Thanh Nhan

Tóm tắt

We study the long time behavior of solutions of gradient-like systems that admit a strict Lyapunov function. In a recent paper of Merlet and Nguyen [11], the authors showed that if the Lyapunov function satisfies the Kurdyka-Lojasiewicz inequality then the convergence result can be obtained by the angle condition. In this paper, we extend this result by taking a weaker angle condition which was proposed by Huang in [6]. The convergence rates are also obtained under some additional hypotheses.

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Tạp chí của Trường Đại học Sư phạm Thành phố Hồ Chí Minh ; ISSN: 1859 -3100