Exact null controllability of a semilinear parabolic equation arising infinance

摘要

This paper is concerned with the exact null controllability of certain semilinearBlack–Scholes type equations in a bounded interval of R± with Neumann boundaryconditions. The control is assumed to be distributed along a subset w of I. First, weprove the exact null controllability of an associated linearized problem by establishing theobservability estimate derived from a Carleman type inequality which is the key result forthe whole theory. Then, the exact null controllability of the nonlinear problem is discussedusing the infinite-dimensional Kakutani fixed point theorem.