An Overview of the Hamilton-jacobi Equation
نویسنده
چکیده
This paper is a survey of the Hamilton-Jacobi partial differential equation. We begin with its origins in Hamilton’s formulation of classical mechanics. Next, we show how the equation can fail to have a proper solution. Setting this issue aside temporarily, we move to a problem of optimal control to show another area in which the equation arises naturally. In the final section, we present some modern theory of the equation. We define a viscosity solution to the PDE and describe some of its properties. We conclude by bringing together ideas developed in the earlier sections.
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