Partial differential equations contrast structures

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. 

The mathematics of thermodynamics is, in fact, extremely simple, apart from a few special casts, and consists mainly of the methods of partial differentiation and of ordinary differential equations of simple form. The conceptual aspect of thermodynamics is, in contrast, extraordinary abstract and it is here that the real difficulties arise. It has long been customary to try to avoid these difficulties by means of spurious analogies. It has, however, become clear that this method makes a deeper understanding leading to mastery of the subject more difficult. The characteristic properties of this field must be accepted and, on the one hand, basic concepts must be developed from concrete experience while, on the other, the mathematical structure must be analyzed. These consideration determine the way in which tins book is written. 

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