AN ELEMENTARY APPROACH TO A MODEL PROBLEM OF LAGERSTROM

The equation studied is $u^{\prime\prime}+\frac{n-1}{r}u^{\prime}+\varepsilon u\,u^{\prime}+ku^{\prime2}=0$, with boundary conditions $u\left(1\right)=0$, $u\left(\infty\right) =1$. This model equation has been studied by many authors since it was introduced in the 1950s by P. A. Lagerstrom. We use...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 2009-01, Vol.40 (6), p.2421-2436
Main Authors: HASTINGS, S. P, MCLEOD, J. B
Format: Article
Language:English
Subjects:
Applied mathematics
Asymptotic expansions
Boundary conditions
Boundary value problems
Exact sciences and technology
Infinite series
Matching
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Proving
Sciences and techniques of general use
Uniqueness
Citations: Items that this one cites
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Summary:The equation studied is $u^{\prime\prime}+\frac{n-1}{r}u^{\prime}+\varepsilon u\,u^{\prime}+ku^{\prime2}=0$, with boundary conditions $u\left(1\right)=0$, $u\left(\infty\right) =1$. This model equation has been studied by many authors since it was introduced in the 1950s by P. A. Lagerstrom. We use an elementary approach to show that there is an infinite series solution which is uniformly convergent on $1\leq r0$, $k\geq0$, and $n\geq1$.
ISSN:0036-1410
1095-7154
DOI:10.1137/080718759