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A note on the oneside exact boundary controllability for quasilinear hyperbolic systems
On a Nested BoundaryLayer Problem
1.  Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States 
2.  Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong 
$\varepsilon^3xy''(x)+x^2y'(x) (x^3+\varepsilon)y(x)=0$ with $0 < x <1$, $y(0) = 1$ and $y(1) = \sqrt{e}$.
An asymptotic solution, which holds uniformly for $x\in [0,1]$, is constructed rigorously. This result also provides an explicit formula for the exponentially small leading term in the interval where the exact solution exhibits such behavior. This henomenon has never been mentioned in the existing literature.
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