ABSTRACT
We considered optimization control problems for linear first order evolutional equations. The example is the classic heat equation. The natural continuation of these results is the analysis of the analogical problems for the nonlinear equations (see Figure 9.1). At first, we consider nonlinear evolutional equations with monotone operators that are the non-stationary analogs of the equations from Chapter 4. We prove the one-valued solvability of the Cauchy problem and weak continuity of its solution with respect to the absolute term. We consider a parabolic equation with nonlinearity power as an example of this system. This is the analog of the stationary equations of Chapter 4 and Chapter 5 (see Figure 9.1).
