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Progress in the Theory of Nonlinear Diffusion: Asymptotics via Entropy Methods

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Trends in Contemporary Mathematics

Part of the book series: Springer INdAM Series ((SINDAMS,volume 8))

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Abstract

We report on recent progress in the study of nonlinear diffusion equations in which the author has been involved. The main topic we discuss here is the use of entropy methods to obtain a precise description of the asymptotic behaviour of the solutions of evolution problems posed in the whole space. A detailed account is given of the analysis of the fast diffusion flow for low values of the equation exponent, which entails a delicate entropy analysis via weighted linearization. Connections and extensions are mentioned.

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Acknowledgements

Work partially supported by Spanish Project MTM2011-24696 (Spain).

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Juan Luis Vázquez

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  1. Juan Luis Vázquez
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Correspondence to Juan Luis Vázquez .

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Editors and Affiliations

  1. Istituto Nazionale di Alta Matematica "Francesco Severi", Roma, Italy

    Vincenzo Ancona

  2. Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Roma, Italy

    Elisabetta Strickland

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Vázquez, J.L. (2014). Progress in the Theory of Nonlinear Diffusion: Asymptotics via Entropy Methods. In: Ancona, V., Strickland, E. (eds) Trends in Contemporary Mathematics. Springer INdAM Series, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-05254-0_9

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