Time dependent \(m\)-accretive operators generating differential evolutions (Q1174553)

This article deals with the equation \[ x'(t)+A(t)x(t)\ni 0\qquad (0\leq t\leq T) \] with \(m\)-\(\omega\)-accretive operator-valued function \(A(t): {\mathcal D}(A(t))\subseteq X\to 2^ X\) where \(X\) is a Banach space with uniformly convex dual \(X^*\). The main result is the existence theorem for strong solutions to the equation above under the condition that Yosida approximations \(A_ \lambda(t)\) for \(A(t)\) have some special properties (these properties guarantee ``good properties'' of the original equation only when \(t\) increases). Some examples for the heat and wave equations with nonlinear boundary conditions are given as simple applications of the abstract results.