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- W2023530101 abstract "The jumps of solutions of the boundary value problem $varepsilon x'' = g(x)f(x')$$c < t < d$$x(c) = a$, $x(d) = b$ are studied for a small, positive $varepsilon $. Using continuity arguments, solutions with a free layer at $t_0 $ are found for all $t_0 in (c,d)$ and the position of $t_0 $ as a function of $varepsilon $ and of the boundary conditions is given. A new phenomenon appears as a consequence of the sensitive dependence of $t_0 $ on the boundary data. For certain values of a and b the location of $t_0 $ changes rapidly on $[c,d]$. There is a sharp transition between solutions with boundary layers at c and those with boundary layers at d. The set of $(a,b)$ for which there are free layers is given. Nonstandard analysis methods and the geometrical approach of the observability plane are used." @default.
- W2023530101 created "2016-06-24" @default.
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- W2023530101 date "1990-09-01" @default.
- W2023530101 modified "2023-09-24" @default.
- W2023530101 title "Free Layers in a Singularly Perturbed Boundary Value Problem" @default.
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- W2023530101 doi "https://doi.org/10.1137/0521070" @default.
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