2021-06-242021-06-242016Vázquez Valenzuela, R. y Krstic, M. (2016). Boundary control of a singular reaction-diffusion equation on a disk. En IFAC Workshop on Control of Systems Governed by Partial Differential Equations (74-79), Bertinoro, Italia: Elsevier.2405-8963https://hdl.handle.net/11441/114808Recently, the problem of boundary stabilization for unstable linear constant-coefficient reaction-diffusion equation on n-balls (in particular, disks and spheres) has been solved by means of the backstepping method. However, the extension of this result to spatially-varying coefficients is far from trivial. As a first step, this work deals with radially-varying reaction coefficients under revolution symmetry conditions on a disk (the 2-D case). Under these conditions, the equations become singular in the radius. When applying the backstepping method, the same type of singularity appears in the backstepping kernel equations. Traditionally, well-posedness of the kernel equations is proved by transforming them into integral equations and then applying the method of successive approximations. In this case, the resulting integral equation is singular. A successive approximation series can still be formulated, however its convergence is challenging to show due to the singularities. The problem is solved by a rather non-standard proof that uses the properties of the Catalan numbers, a well-known sequence frequently appearing in combinatorial mathematics.application/pdf6 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Boundary controlReaction-diffusion equationinfo:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/openAccess10.1016/j.ifacol.2016.07.42120978115