Complex variable methods applied to free boundary problems
Time and place
1 PM on Thursday, November 15th, 2007; NAC 1/511E (Artino Lab)
Linda Cummings (Nottingham)
Abstract
Complex variable methods such as conformal mapping can be usefully applied to a variety of 2D free (and moving) boundary problems where the governing equation is Laplacian or biharmonic. We illustrate how exact time-dependent solutions can be obtained for a classical problem from fluid mechanics: the Hele-Shaw free boundary problem. This problem, which arises from a very simple experimental set-up, is mathematically equivalent to many physically-relevant situations.
After introducing the Hele-Shaw experimental set-up and governing equations, the complex variable methods will be explained, and demonstrated by examples. Issues of solution breakdown (and how to prevent this mathematically) will be discussed. If time permits, application of similar methods to other physically-relevant free boundary problems will be outlined.
