A dynamic programming approach to nonlinear boundary control problems of parabolic type

Piermarco Cannarsa, Fausto Gozzi, Halil Mete Soner

Research output: Contribution to journalArticle

21 Scopus citations

Abstract

In this paper we study a Hamilton-Jacobi equation related to the boundary control of a parabolic equation with Neumann boundary conditions. The state space of this problem is a Hilbert space and the equation is defined classically only on a dense subset of the state space. Moreover the Hamiltonian appearing in the equation contains fractional powers of an unbounded operator. These facts render the problem difficult. In this paper we give a revised definition of a viscosity solution to accommodate the unboundness of the Hamiltonian. We then obtain existence and uniqueness results for viscosity solutions. In particular we show that under suitable assumptions the value function of the boundary control problem is the unique viscosity solution of the related Hamilton-Jacobi equation.

Original languageEnglish (US)
Pages (from-to)25-61
Number of pages37
JournalJournal of Functional Analysis
Volume117
Issue number1
DOIs
StatePublished - Oct 1993
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis

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