Book chapter
Some Examples
Dynamics with Inequalities, pp.1-16
Other Titles in Applied Mathematics, Society for Industrial and Applied Mathematics
01/01/2011
DOI: 10.1137/1.9781611970715.ch1
Abstract
… there is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician.
Daniel Bernoulli
In this chapter we see how a number of differential equations with inequalities arise. The inequalities that arise are naturally in the form of complementarity problems or in variational inequalities. These may arise from variational principles or from simple principles of the form “if this is positive, then that must be zero.” There are more general formulations of hybrid systems which consist of a system of differential equations together with rules of the kind “when we are in this (discrete) state and we reach this set, then we change our state to another and continue with the corresponding differential equation.” Such models may appear attractive to engineers, because this corresponds closely to how a system might be programmed. But there are a number of problems with this approach.
Details
- Title: Subtitle
- Some Examples
- Creators
- David E Stewart - University of Iowa
- Resource Type
- Book chapter
- Publication Details
- Dynamics with Inequalities, pp.1-16
- Series
- Other Titles in Applied Mathematics
- DOI
- 10.1137/1.9781611970715.ch1
- Publisher
- Society for Industrial and Applied Mathematics
- Language
- English
- Date published
- 01/01/2011
- Academic Unit
- Mathematics
- Record Identifier
- 9984242443002771
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