Existence of optimal solutions together with first-order and necessary/sufficient second-order optimality conditions are established for pointwise tracking optimal control of a fractional semilinear elliptic PDE.
Roub ´ıˇcek (2013),Nonlinear partial differential equations with applications, Second, vol
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Existence and uniqueness of weak solutions are proved for the semilinear time-dependent equation with second or fourth order diffusion and cubic nonlinearity, for both smooth and rough initial data via Faedo-Galerkin and compactness methods.
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Existence of optimal solutions together with first-order and necessary/sufficient second-order optimality conditions are established for pointwise tracking optimal control of a fractional semilinear elliptic PDE.
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