Contingent solutions for the Bellmann equation in infinite dimensions (Q1584021)

The author considers the minimum time problem for an infinite dimensional linear control system on a reflexive Banach space. Under certain conditions (among which is the continuity of the optimal control function at \(t=0\)) the author proves that the minimum time function as well as its Kruzkov transformation are contingent solutions of the respective Hamilton-Jacobi-Bellman equations. An important ingredient of the proof are viability properties of the hypograph of the minimum time functions under the semigroup generated by the considered system.