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Hamilton-Jacobi equations for control problems of parabolic equations

Sophie GombaoJean-Pierre Raymond — 2006

ESAIM: Control, Optimisation and Calculus of Variations

We study Hamilton-Jacobi equations related to the boundary (or internal) control of semilinear parabolic equations, including the case of a control acting in a nonlinear boundary condition, or the case of a nonlinearity of Burgers' type in 2D. To deal with a control acting in a boundary condition a fractional power ( - A ) β – where is an unbounded operator in a Hilbert space – is contained in the Hamiltonian functional appearing in the Hamilton-Jacobi equation. This situation has already been studied...

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