Duality and nonlinear equations governed by accretive operators. (English) Zbl 0766.47029

Many nonlinear evolution equations which can be solved using semigroups generated by accretive operators in Banach spaces have dual equations which can be solved in the same way. The author studies this phenomenon by examining conditions under which accretivity of \(AB\) implies accretivity of \(B^ tA^ t\), where the concept of adjoint operator is appropriately extended. Included are cases where the operators \(A\) and \(B\) are linear symmetric coercive operators, subdifferentials, or monotone operators in Hilbert spaces. Examples are presented to show applications of the results as well as alternative methods.


47H06 Nonlinear accretive operators, dissipative operators, etc.
47H20 Semigroups of nonlinear operators