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On the Theoretical and Numerical Control of a One-Dimensional Nonlinear Parabolic Partial Differential Equation
Authors:Enrique Fernández-Cara  Dany Nina-Huamán  Miguel R Nuñez-Chávez  Franciane B Vieira
Institution:1.Dpto. E.D.A.N.,Universidad de Sevilla,Sevilla,Spain;2.IME, Univ. Federal Fluminense, Rua Professor Marcos Waldemar de Freitas Reis,Niterói,Brazil;3.Dpto. Matemática,Universidade Federal do Piauí, Campus Universitário Ministro Petr?nio Portella,Teresina,Brazil
Abstract:This paper deals with the analysis of the internal and boundary control of a one-dimensional parabolic partial differential equation with nonlinear diffusion. First, we prove a local null controllability result with distributed controls, locally supported in space. The proof relies on local inversion (more precisely, we use Liusternik’s Inverse Function Theorem), together with some appropriate specific estimates. We also establish a similar result with controls on one side of the boundary. Then, we consider an iterative algorithm for the computation of null controls, we prove the convergence of the iterates, and we perform some numerical experiments.
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