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Wellposedness of Semilinear Heat Equations with Iterated Logarithms
Exponential Bases in Sobolev Spaces in Control and Observation Problems
Discretization of the Controllability Grammian
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1999 Birkhauser Verlag adjoint Algorithm analytic applied approximate controllability assume assumptions Birkhauser Verlag Basel/Switzerland boundary conditions boundary control boundary value problem bounded compact computation consider constant convergence convex cost functional decomposition defined denotes derivative differential equations discretization dxdt E-mail address elastic elliptic estimate exact controllability exists exponential exponential family formulation given holds implies inequality initial condition initial data ISNM Lasiecka Lemma linear Lipschitz continuous mapping Math Mathematics matrix Moreover multigrid methods Naghdi's Nash equilibrium Navier-Stokes equations nonlinear norm numerical obtain operator optimal control optimality conditions optimization problem paper parabolic parameter partial differential equations plate proof of Theorem Proposition prove regularity respect result Riesz basis satisfies Schur complement second order semigroup semilinear sequence shape optimization shell smooth Sobolev spaces Sprekels stability subset tensor Theorem 3.1 theory thermoelastic Troltzsch unique solution vector field wave equation weakly zero Zolesio