On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator

الملخص EN

For the evolution equation y′(t)=Ay(t) with a scalar type spectral operator A in a Banach space, conditions on A are found that are necessary and sufficient for all weak solutions of the equation on [0,∞) to be strongly infinite differentiable on [0,∞) or [0,∞).

Certain effects of smoothness improvement of the weak solutions are analyzed.