Bodart, OlivierGonzález Burgos, ManuelPérez García, Rosario2016-05-232016-05-232004Bodart, O., González Burgos, M. y Pérez García, R. (2004). A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions. SIAM Journal on Control and Optimization, 43 (3), 955-969.0363-01291095-7138http://hdl.handle.net/11441/41470In this paper we present a local result on the existence of insensitizing controls for a semilinear heat equation when nonlinear boundary conditions of the form ∂ny + f(y)=0 are considered. The problem leads to an analysis of a special type of nonlinear null controllability problem. A sharp study of the linear case and a later application of an appropriate fixed point argument constitute the scheme of the proof of the main result. The boundary conditions we are dealing with lead us to seek a fixed point, and thus also control functions, in certain H¨older spaces. The main strategy in this paper is the construction of controls with H¨olderian regularity starting from L2-controls in the linear case. Sufficient regularity in the data and appropriate assumptions on the right-hand side term ξ of the equation are required.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/controllabilitynonlinear PDE of parabolic typeinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1137/S036301290343161X