ABSTRACT
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 6.1 Newton’s Law of Heating and Cooling Subjected to Polynomial Effects . . . . . . 153 6.2 Pharmocokinetics with Concentration-Dependent Dosing . . . . . . . . . . . . . . . . . . . . . 155 6.3 Springs with Nonlinear Restoring Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 6.4 Circuits with Quadratic Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 6.5 Enyzme Catalysts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 6.6 Projectile Motion-Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 6.7 Floor Displacement Model with Nonlinear Shock Absorbers . . . . . . . . . . . . . . . . . . 163
The non-homogeneous models considered in the previous two chapters constitute a first attempt at incorporating external forces affecting a system into a description of its evolution. While it is the case that some perturbations can be described accurately and meaningfully using such simple function of t, the truth is the development of the theory for (Non-CP) primarily serves as a hub in the formulation of a richer theory of so-called semilinear Cauchy problems in which the forcing term describes nonlinear interaction effects among the various components of the solution vector. We will use the theory developed in Chapters 4 and 5 as a springboard in our discussion in the next two chapters. For the moment, we introduce specific scenarios, identify a common connective theme, and then uncover subtleties that throw a veritable wrench into the works as we formulate a generalization of the theory in Chapter 5 to handle these new models.
