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Global Null Controllability of the 1-Dimensional Nonlinear Slow Diffusion Equation

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Abstract

The authors prove the global null controllability for the 1-dimensional nonlinear slow diffusion equation by using both a boundary and an internal control. They assume that the internal control is only time dependent. The proof relies on the return method in combination with some local controllability results for nondegenerate equations and rescaling techniques.

Keywords

Nonlinear control Nonlinear slow diffusion equation Porous medium equation 

Mathematics Subject Classification

35L65 35L567 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.UMR 7598 Laboratoire Jacques-Louis LionsInstitut Universitaire de France and Université Pierre et Marie Curie (Paris 6)Paris cedex 5France
  2. 2.Instituto de Matemática Interdisiplinar and Dpto. de Matemática AplicadaUniversidad Complutense de MadridMadridSpain
  3. 3.UMR 7598 Laboratoire Jacques-Louis LionsUniversité Pierre et Marie Curie (Paris 6)Paris cedex 5France
  4. 4.Dpto. de Matemática AplicadaUniversidad Complutense de MadridMadridSpain

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