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Ishii, Hiroyuki

Boundary and interior transition layer phenomena. I. (English) Zbl 0649.34026

Sci. Rep. Fac. Educ., Fukushima Univ. 37, 1-7 (1986).

We consider the boundary value problems for system with a small parameter \(\epsilon >0\). This system is made of differential equations for two unknown functions and the parameter \(\epsilon^ 2\) is multiplying the heighest derivatives of these unknown functions. The independent variable t is contained explicitly.
It is necessary to generalize the theory by P. Fife [J. Math. Anal. Appl. 54, 497-521 (1976; Zbl 0345.34044)] when we consider the asymptotic properties of a given boundary value problem under the above conditions.
We generalize the results of P. Fife (loc. cit.) and we show the existence of a solution which exhibits the boundary and interior transition layer phenomena as \(\epsilon\to 0\). And we grasp the asymptotic behavior of this solution by \(L_ 1\)-norm.

Cited in 1 Review

MSC:

34B10

Nonlocal and multipoint boundary value problems for ordinary differential equations

Keywords:

small parameter; asymptotic properties; existence; transition layer; asymptotic behavior

Citations:

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