Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2009-01-20
Nonlinear Sciences
Exactly Solvable and Integrable Systems
27 pages
Scientific paper
10.1007/s11785-008-0093-7
The planar elliptic extension of the Laplacian growth is, after a proper parametrization, given in a form of a solution to the equation for area-preserving diffeomorphisms. The infinite set of conservation laws associated with such elliptic growth is interpreted in terms of potential theory, and the relations between two major forms of the elliptic growth are analyzed. The constants of integration for closed form solutions are identified as the singularities of the Schwarz function, which are located both inside and outside the moving contour. Well-posedness of the recovery of the elliptic operator governing the process from the continuum of interfaces parametrized by time is addressed and two examples of exact solutions of elliptic growth are presented.
Khavinson Dmitry
Mineev-Weinstein Mark
Putinar Mihai
No associations
LandOfFree
Planar elliptic growth does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Planar elliptic growth, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Planar elliptic growth will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-435474