A PRIORI BOUNDS AND WELL-POSEDNESS OF A SYSTEM ASSOCIATED WITH UNSTEADY BOUNDARY LAYER FLOWS

Guang Chong Yang; Hua Bing Feng

doi:10.11948/2015008

2015 Volume 5 Issue 1

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Guang Chong Yang, Hua Bing Feng. A PRIORI BOUNDS AND WELL-POSEDNESS OF A SYSTEM ASSOCIATED WITH UNSTEADY BOUNDARY LAYER FLOWS[J]. Journal of Applied Analysis & Computation, 2015, 5(1): 89-102. doi: 10.11948/2015008

Citation:

Guang Chong Yang, Hua Bing Feng. A PRIORI BOUNDS AND WELL-POSEDNESS OF A SYSTEM ASSOCIATED WITH UNSTEADY BOUNDARY LAYER FLOWS[J]. Journal of Applied Analysis & Computation, 2015, 5(1): 89-102. doi: 10.11948/2015008

A PRIORI BOUNDS AND WELL-POSEDNESS OF A SYSTEM ASSOCIATED WITH UNSTEADY BOUNDARY LAYER FLOWS

College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, Sichuan, China

Fund Project:

Abstract

Abstract

An integral equation with singularities is introduced to characterize unsteady laminar boundary layer flows and some properties of solutions of this integral equation are investigated. Utilizing these properties, a priori bounds are obtained for the skin friction function and the similarity stream function and the well-posedness of solutions is proved.
- Boundary layer /
- unsteady flows /
- nonautonomous /
- a priori bounds /
- well-posedness
MSC: 76D10;34B16;34B16;34B40;49K40

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References

[1]	H.I. Andersson, J.B. Aarseth and B.S. Dandapat, Heat transfer in a liquid film on an unsteady stretching surface, Int. J. Heat Mass Tran., 43(2000), 69-74. Google Scholar
[2]	A.H. Fatheah and H. Majid, Analytic solution for MHD Falkner-Skan flow over a Pourous Surface, J. Appl. Math., 2012, Article ID123185. Google Scholar
[3]	M. Guedda, Emad H. Aly and A. Ouahsine, Analytical and ChPDM analysis of MHD mixed convection over a vertical flat plate embedded in a porous medium filled with water at 4° C, Appl. Math. Model., 35(2011), 5182-5197. Google Scholar
[4]	M. Guedda and A. Ouahsine, Similarity solutions of MHD flow in a saturated porous medium, Eur. J. Mech. B-Fluid, 33(2012), 87-94. Google Scholar
[5]	A. Ishak, R. Nazar and I. Pop, Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature, Nonlinear Analysis(RWA), 10(2009), 2909-2913. Google Scholar
[6]	S.M. Imran, S. Asghar and M. Mushtaq, Mixed convection flow over an unsteady stretching surface in a porous medium with heat source, Math. Probl. Eng., 2012, Article ID485418. Google Scholar
[7]	K.Q. Lan and G.C. Yang, Positive solutions of the Falkner-Skan equation arising in the boundary layer theory, Canad. Math. Bull., 51(3)(2008), 386-398. Google Scholar
[8]	O.D. Makinde and A. Aziz, MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition, Int. J. Therm. Sci., 49(2010), 1813-1820. Google Scholar
[9]	J.E. Paullet, Analysis of fluid flow and heat transfer over an unsteady stretching surface, Nonlinear Analysis(TMA), 75(2012), 4079-4089. Google Scholar
[10]	K. Schrader, A generalization of the Helly selection theorem, Bull. Amer. Math. Soc., 78(3)(1972), 415-419. Google Scholar
[11]	K. Vajravel, K.V. Prasad and Chiu-On Ng, Unsteady convective boundary layer flow of a viscous fluid at a vertical surface with variable fluid properties, Nonlinear Analysis(RWA), 14(2013), 455-464. Google Scholar
[12]	C.Y. Wang, Similarity stagnation point solutions of the Navier-Stokes equations-review and extension, Eur. J. Mech. B-Fluid, 27(2008), 678-683. Google Scholar
[13]	C.Y. Wang, Review of similarity stretching exact solutions of the Navier-Stokes equations, Eur. J. Mech. B-Fluid, 30(2011), 475-479. Google Scholar
[14]	G.C. Yang and K.Q. Lan, Nonexistence of the reversed flow solutions of the Falkner-Skan equations, Nonlinear Analysis(TMA), 74(2011), 5327-5339. Google Scholar
[15]	G.C. Yang and K.Q. Lan, Systems of singular intergal equations and applications to existence of revised flow solutions of Falkner-Skan equations, Comm. Pure Appl. Anal., 12(2013), 2465-2495. Google Scholar
[16]	G.C. Yang, L. Zhang and L.F. Dang, Existence and nonexistence of solutions on opposing mixed convection problems in boundary layer theory, Eur. J. Mech. B-Fluid, 43(2014), 148-153. Google Scholar
[17]	G.C. Yang and K.Q. Lan, The velocity and shear stress functions of the Falkner-Skan equation arising in boundary layer theory, J. Math. Anal. Appl., 328(2)(2007), 1297-1308. Google Scholar
[18]	Z. Ziabakhsh, G. Domairry, M. Mozaffari and M. Mahbobifar, Analytical solution of heat transfer over an unsteady stretching surface with prescribed wall temperature, J. Taiwan Inst. Chem. Eng., 41(2010), 169-177. Google Scholar