Sensitivity of the climatic system mathematical methods of analysis

We consider the available mathematical methods of analysis of sensitivity, using as an example a dynamic system governed by the equation dy/dt = v(y,a). (6.1.1)

In the simplest situations the state y of the system and the parameter a are finite-dimensional vectors. We shall also consider the more general case where, for any a, the vector y is a function of the spatial variables x changing in a domain Q. In the general case the phase space Y of the system (6.1.1) is infinite dimensional. If the field v is specified by a differential operator, its description has to include the information about boundary conditions ensuring single-valued solvability of the Cauchy problem for Equation (6.1.1). Let us denote the resolving operators by v'a so that the solution to the Cauchy problem with an initial condition y|r=0 = y0 will be defined by the formula

0 0

Post a comment