Symmetries and heir equations for the laminar boundary layer model
type: Item
instance of: scholarly article
title: Symmetries and heir equations for the laminar boundary layer model
zbMATH Open document ID: 0865.35024
author: F. Allassia
author: M. C. Nucci
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-07-10T00:00:00Z
review text: The nonclassical symmetry method for finding exact solutions of partial differential equations consists in postulating a new requirement (the invariant surface condition) compatible with the primary system of equations. This compatibility condition with uncertain coefficients yields another (heir) system, and the procedure can be repeated. Using this method, the authors precisely analyze explicit solutions of the Prandtl system \[ uu_x+ vu_y=w_y,\quad u_x+v_y=0,\quad u_y=w \] governing an incompressible viscous fluid moving near a thin plate with steady flow and zero pressure gradient. Calculations are stated with details up to third iteration, and interrelations to the classical Lie algebra invariance are discussed.
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 76D10
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 930230
zbMATH Keywords: nonclassical symmetries method
zbMATH Keywords: Prandtl system
zbMATH Keywords: Lie algebra invariance
reviewed by: Jan Chrastina
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0292
OpenAlex ID: W2016072260
DOI: 10.1006/JMAA.1996.0292
description: scientific article; zbMATH DE number 930230