CLASS OF NONSINGULAR EXACT-SOLUTIONS FOR LAPLACIAN PATTERN-FORMATION

Authors
MINEEVWEINSTEIN MB DAWSON SP
Citation
Mb. Mineevweinstein et Sp. Dawson, CLASS OF NONSINGULAR EXACT-SOLUTIONS FOR LAPLACIAN PATTERN-FORMATION, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 50(1), 1994, pp. 180000024-180000027
Citations number
31
Categorie Soggetti
Physycs, Mathematical","Phsycs, Fluid & Plasmas
Journal title
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics → ACNP
ISSN journal
1063651X
Volume
50
Issue
1
Year of publication
1994
Pages
180000024 - 180000027
Database
ISI
SICI code
1063-651X(1994)50:1<180000024:CONEFL>2.0.ZU;2-X
Abstract
We present a class of exact solutions for the so-called Laplacian grow th equation describing the zero-surface-tension limit of a variety of two-dimensional pattern formation problems. These solutions are free o f finite-time singularities (cusps) for quite general initial conditio ns. They reproduce various features of viscous fingering observed in e xperiments and numerical simulations with surface tension, such as exi stence of stagnation points, screening, tip splitting, and cooarsening . In certain cases the asymptotic interface consists of N separated mo ving Saffman-Taylor fingers.