Global controllability properties for the semilinear heat equation with superlinear term (Q1974111)

This paper concerns some global approximate controllability properties for the semilinear heat equation with superlinear reaction-convection term, governed in a bounded domain by locally distributed controls as well as the steering of the projections of its solution on any finite-dimensional space spanned by the eigenfunctions for the truncated linear part. It is shown that if the control-supporting area is properly chosen, then they can approximately be controlled globally at any time in the topology induced by \(L^2(\Omega)\). It is also proved that if the nonlinearity is purely of reaction type and is locally Lipschitz, then the global exact controllability in finite dimensions holds as well.