2018/10/13 by Junya Nishiguchi, Nishiguchi, Junya
Computer Science · Engineering · #34K30 #37L05 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Primary: 34K05 #Secondary: 37B55 #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1810.05890
openalex publication_date 2018/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we establish a theory of well-posedness for delay differential equations (DDEs) via notions of prolongations and C1-prolongations, which are continuous and continuously differentiable extensions of histories to the right, respectively. In this sense, this paper serves as a continuation and an extension of the previous paper by this author (\citeNishiguchi 2017). The results in \citeNishiguchi 2017 are applicable to various DDEs, however, the results in \citeNishiguchi 2017 cannot be applied to general class of state-dependent DDEs, and its extendability is missing. We find this missing link by introducing notions of (C1-) prolongabilities, regulation of topology by (C1-) prolongations, and Lipschitz conditions about (C1-) prolongations, etc. One of the main result claims that the continuity of the semiflow with a parameter generated by the trivial DDEs x = v plays an important role for the well-posedness. The results are applied to general class of state-dependent DDEs.