Abstract
We have seen in Chapter II that even restricting ourselves to a few relatively simple-looking ordinary differential equations we get a great variety of types of expansions when applying singular perturbation techniques. Also, as seen in Chapter II, Section 4, replacing the middle term in eu″ + u x — u = 0 by the quasi-linear term uu x greatly increases the variety of solutions for two-point boundary value problems. Obviously, we expect the variety of solutions and the techniques necessary to be very large when we consider partial differential equations.
In this chapter we shall use some terminology and theorems which are standard in the theory of partial differential equations. Since there are many textbooks on this subject no particular reference is given.
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© 1988 Springer Science+Business Media New York
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Lagerstrom, P.A. (1988). Layer-type Problems. Partial Differential Equations. In: Matched Asymptotic Expansions. Applied Mathematical Sciences, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1990-1_3
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DOI: https://doi.org/10.1007/978-1-4757-1990-1_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3086-6
Online ISBN: 978-1-4757-1990-1
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