Spike-type contrast structures solutions

Construction of an Asymptotic Expansion for the Parabolic Problem Other Problems with Corner Boundary Layers Nonisothermal Fast Chemical Reactions Contrast Structures in Partial Differential Equations A. Step-Type Solutions in the Noncritical Case Step-Type Solutions in the Critical Case Spike-Type Solutions Applications... 

Contrast structures of step type and spike t) pe were considered in Section V for ordinary differential equations. In this section, we construct asymptotics for step-type and spike-type solutions of partial differential equations. 

We retain condition III from Section VIII.A, which is required for the construction of the boundary functions. Under conditions I-III we construct an asymptotic expansion for a spike-type solution or, in other words, for a contrast spike-type structure. This is a solution of problem (8.1), (8.2), which is close to the solution u = closed curve F where the solution has a spike. The location of the curve r is not known a priori just as in Section VIII.B. This curve is defined during the construction of the asymptotics. 

Thus we see that these solutions have not only boundary layers, but also interior layers. Solutions having such interior layers are called contrast structures. A contrast structure of the type represented in Fig. 8 is called a spike, and a contrast structure of the type represented in Fig. 9 is called a step (or threshold). 

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See also in sourсe #XX -- [ , , , ]

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