On the strong smoothness of weak solutions of an abstract evolution equation ii. gevrey ultradifferentiability

Abstract

For the evolution equation

with a normal operator A in a Hilbert space, conditions on A are found necessary and sufficient for all weak solutions of the equation on [0,∞) to be strongly ultradifferentiable in the Gevrey sense (in particular, real analytic or entirej. Certain effects of smoothness improvement of the weak solutions are analyzed. The real analyticity/entireness of weak solutions of the equation with a symmetric/semibounded below operator is proved.

Keywords:

• Weak solution
• normal operator
• Gevrey classes

Keywords:

• 34G10
• 17B15
• 37D06