Super polyharmonic property of solutions for PDE systems and its applications
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A Brezis-Nirenberg result for non-local critical equations in low dimension
November 2013, 12(6): 2465-2495. doi: 10.3934/cpaa.2013.12.2465
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,
Department of Computation Science, Chengdu University of Information Technology, Chengdu, Sichuan 610225, China
Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3, Canada
Received May 2012 Revised December 2012 Published May 2013
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.
Keywords: reversed flow solutions, Schauder fixed point theorem, Falkner-Skan equation, boundary layer equations., System of singular integral equations, Helly selection theorem.
Mathematics Subject Classification: Primary: 34B16, 34B40; Secondary: 47H10, 76D1.
Citation: G. C. Yang, K. Q. Lan. Systems of singular integral equations and applications to existence of reversed flow solutions of Falkner-Skan equations. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2465-2495. doi: 10.3934/cpaa.2013.12.2465
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G. C. Yang K. Q. Lan