Feedback controllability for blowup points of semilinear heat equations
Ping Lin
Discrete & Continuous Dynamical Systems - B 2017, 22(4): 1425-1434 doi: 10.3934/dcdsb.2017068

This paper studies a controllability problem for blowup points of two classes of semilinear heat equations.Our goal to act controls on the systems we studied is to make the corresponding solutions blow upat given points. This differs with the controllability problem of equations with the property of blowup in the references, where the purpose of using controls is to prevent blowupby controls. We obtain the feedback controls for our controllability problem of blowup points.

keywords: Blowup point semilinear heat equation feedback controllability for blowup point
Retinal vessel segmentation using a finite element based binary level set method
Zhenlin Guo Ping Lin Guangrong Ji Yangfan Wang
Inverse Problems & Imaging 2014, 8(2): 459-473 doi: 10.3934/ipi.2014.8.459
In this paper we combine a few techniques to label blood vessels in the matched filter (MF) response image by using a finite element based binary level set method. An operator-splitting method is applied to numerically solve the Euler-Lagrange equation from minimizing an energy functional. Unlike the traditional MF methods, where a threshold is difficult to be selected, our method can automatically get more precise blood vessel segmentation using an enhanced edge information. In order to demonstrate the good performance, we compare our method with a few other methods when they are applied to a publicly available standard database of coloured images (with manual segmentations available too).
keywords: operator-splitting. Retinal vessel segmentation binary level set method
Optimal control problems for some ordinary differential equations with behavior of blowup or quenching
Ping Lin Weihan Wang
Mathematical Control & Related Fields 2018, 8(3&4): 809-828 doi: 10.3934/mcrf.2018036

This paper is concerned with some optimal control problems for equations with blowup or quenching property. We first study the existence and Pontryagin's maximum principle for optimal controls which have the minimal energy among all the controls whose corresponding solutions blow up at the right-hand time end-point of a given functional. Then, the same problem for quenching case is discussed. Finally, we establish Pontryagin's maximum principle for optimal controls of extended problems after quenching.

keywords: Optimal control ordinary differential equations blowup quenching

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