Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Asymptotic behavior of solutions to a BVP from fluid mechanics

Authors: Susmita Sadhu and Joseph E. Paullet
Journal: Quart. Appl. Math. 72 (2014), 703-718
MSC (2010): Primary 34B15, 34B40, 34D05; Secondary 76S05, 76R10
DOI: https://doi.org/10.1090/S0033-569X-2014-01359-X
Published electronically: September 26, 2014
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Abstract: In this paper we investigate a boundary value problem (BVP) derived from a model of boundary layer flow past a suddenly heated vertical surface in a saturated porous medium. The surface is heated at a rate proportional to $ x^k$ where $ x$ measures distance along the wall and $ k>-1$ is constant. Previous results have established the existence of a continuum of solutions for $ -1<k<-1/2$. Here we further analyze this continuum and determine that precisely one solution of this continuum approaches the boundary condition at infinity exponentially while all others approach algebraically. Previous results also showed that the solution to the BVP is unique for $ -1/2 \leq k <0$. Here we extend the range of uniqueness to $ 0\leq k \leq 1$. Finally, the physical implications of the mathematical results are discussed and a comparison is made to the solutions for the related case of prescribed surface temperature on the surface.

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Additional Information

Susmita Sadhu
Affiliation: Department of Mathematics, Georgia College & State University, Milledgeville, Georgia 31061
Email: susmita.sadhu@gcsu.edu

Joseph E. Paullet
Affiliation: School of Science, Pennsylvania State University at Erie, Erie, Pennsylvania 16563
Email: jep7@psu.edu

DOI: https://doi.org/10.1090/S0033-569X-2014-01359-X
Received by editor(s): October 16, 2012
Received by editor(s) in revised form: January 27, 2013
Published electronically: September 26, 2014
Article copyright: © Copyright 2014 Brown University

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