Filters

2008 - 200912010 - 20131

More filters

20192
Reset filters

Settings

Type: Text × Subject: delay-differential equations ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Spectrum and amplitude equations for scalar delay-differential equations with large delay
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Yanchuk, Serhiy; Lücken, Leonhard; Wolfrum, Matthias; Mielke, Alexander
    The subject of the paper are scalar delay-differential equations with large delay. Firstly, we describe the asymptotic properties of the spectrum of linear equations. Using these properties, we classify possible types of destabilization of steady states. In the limit of large delay, this classification is similar to the one for parabolic partial differential equations. We present a derivation and error estimates for amplitude equations, which describe universally the local behavior of scalar delay-differential equations close to the destabilization threshold.
  • Thumbnail Image
    Item
    On a thermomechanical milling model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Chełminski, Krzysztof; Höberg, Dietmar; Rott, Oliver
    This paper deals with a new mathematical model to characterize the interaction between machine and workpiece in a milling process. The model consists of a harmonic oscillator equation for the dynamics of the cutter and a linear thermoelastic workpiece model. The coupling through the cutting force adds delay terms and further nonlinear effects. After a short derivation of the governing equations it is shown that the complete system admits a unique weak solution. A numerical solution strategy is outlined and complemented by numerical simulations of stable and unstable cutting conditions.