12 citations · 25 across the 6 of their papers we have counts for
6 papers
Lemniscates do not survive Laplacian growth
D. Khavinson, M. Mineev-Weinstein, M. Putinar +1
The large class of moving boundary processes in the plane modeled by the so-called Laplacian growth, which describes, e.g., solidification, electrodeposition, viscous fingering, ba…
A note on the extension of the polar decomposition for the multidimensional Burgers equation
Uriel Frisch, Mark Mineev-Weinstein
It is shown that the generalizations to more than one space dimension of the pole decomposition for the Burgers equation with finite viscosity and no force are of the form u = -2 v…
-function for analytic curves
I. K. Kostov, I. Krichever, M. Mineev-Weinstein +2
We review the concept of -function for simple analytic curves. The -function gives a formal solution to the 2D inverse potential problem and appears as the -function of th…
Whitham-Toda Hierarchy in the Laplacian Growth Problem
Mark Mineev-Weinstein, Anton Zabrodin
The Laplacian growth problem in the limit of zero surface tension is proved to be equivalent to finding a particular solution to the dispersionless Toda lattice hierarchy. The hier…
Observation of Conservations Laws in Diffusion Limited Aggregation
Mark B. Mineev-Weinstein, Ronnie Mainieri
We repeat the numerical experiments for diffusion limited aggregation (DLA) and show that there is a potentially infinite set of conserved quantities for the long time asymptotics.…
Multidimensional Pattern Formation Has an Infinite Number of Constants of Motion
Mark B. Mineev--Weinstein
Extending our previous work on 2D growth for the Laplace equation we study here {\it multidimensional} growth for {\it arbitrary elliptic} equations, describing inhomogeneous and a…