ABSTRACT
This chapter presents nonlinear models of epidemics, image restoration, and value of option contracts. In the epidemic model the unknown concentrations of the infected populations will depend on both time and space. Image restoration has applications to satellite imaging, signal processing, and fish finders. The models are based on minimization of suitable real-valued functions whose gradients are similar to the quasi-linear heat diffusion models. The value of option contracts, which are agreements to sell or to buy an item at a future date and given price. The option contract can itself be sold and purchased, and the value of the option contract can be modeled by a partial differential equation that is similar to the heat equation. A portfolio of investments can have a number of assets as well as a variety of option contracts. Option contracts can have more than one underlying asset and different types of payoff functions.
