Systems of  singular integral equations and applications toexistence of reversed flow solutions of Falkner-Skanequations

G. C. Yang; K. Q. Lan

doi:10.3934/cpaa.2013.12.2465

Article Contents

2013, Volume 12, Issue 6: 2465-2495. Doi: 10.3934/cpaa.2013.12.2465

This issue Previous Article A Brezis-Nirenberg result for non-local critical equations in low dimension Next Article Super polyharmonic property of solutions for PDE systems and its applications

Systems of singular integral equations and applications to existence of reversed flow solutions of Falkner-Skan equations

G. C. Yang^1, and
K. Q. Lan^2,

1.
Department of Computation Science, Chengdu University of Information Technology, Chengdu, Sichuan 610225
2.
Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3

Received: May 2012

Revised: December 2012

Published: November 2013

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Abstract

We investigate existence of reversed flow solutions of the Falkner-Skan equations by considering a system of two singular Hammerstein integral equations. We prove that the reversed flow solutions exist for each parameter in $(-1/6,0)$. This is an extension of results on nonexistence of reversed flow solutions obtained recently by the authors. As applications of our new results, we obtain existence of reversed flow similarity solutions of the boundary layer equations governing the flow of fluids over surfaces often arising from engineering problems.

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Mathematics Subject Classification: Primary: 34B16, 34B40; Secondary: 47H10, 76D10.

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