A PDE, or partial differential equation, is a mathematical equation that involves multiple variables and their partial derivatives. It is commonly used to model physical phenomena in fields such as physics, engineering, and economics.
dG/dt represents the partial derivative of the function G with respect to time. This means that the equation is describing how G changes over time.
n, s, and u are all variables in the equation and their meanings may vary depending on the context in which the equation is being used. In general, n could represent a constant or a function, s could represent a spatial variable, and u could represent a function or a constant.
The boundary conditions for a PDE are the conditions that must be specified in order to solve the equation. In this case, the boundary conditions would depend on the specific problem being modeled by the PDE.
There are various methods for solving PDEs, depending on the specific equation and problem being modeled. Some common techniques include separation of variables, method of characteristics, and numerical methods. Consult a textbook or seek assistance from a mathematician or scientist for a specific solution method.