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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
– 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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