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Stability Analysis of Delaunay Surfaces as Steady States for the Surface Diffusion Equation

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Geometric Properties for Parabolic and Elliptic PDE's (GPPEPDEs 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 176))

Abstract

The stability of steady states for the surface diffusion equation will be studied. In the axisymmetric setting, steady states are the Delaunay surfaces, which are the axisymmetric constant mean curvature surfaces. We consider a linearized stability of these surfaces and derive criteria of the stability by investigating the sign of eigenvalues corresponding to the linearized problem.

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Acknowledgments

This work was supported by JSPS KAKENHI Grant Numbers 24540200, 24244012, 25247008. Also I would like to express my gratitude to Professor Miyuki Koiso and Professor Shoji Yotsutani for the fruitful discussion.

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Authors and Affiliations

  1. Graduate School of Maritime Sciences, Kobe University, 5-1-1, Fukae-minamimachi, Higashinada-ku, Kobe, 658-0022, Japan

    Yoshihito Kohsaka

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  1. Yoshihito Kohsaka
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Correspondence to Yoshihito Kohsaka .

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Editors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Milano, Milano, Italy

    Filippo Gazzola

  2. Mathematical Institute, Tohoku University, Sendai, Japan

    Kazuhiro Ishige

  3. Dip. di Matematica e Applicazioni, Università degli Studi di Napoli Federico II, Monte S. Angelo, Napoli, Italy

    Carlo Nitsch

  4. Dipartimento di Matematica Ulisse Dini, Università degli Studi di Firenze, Firenze, Firenze, Italy

    Paolo Salani

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Kohsaka, Y. (2016). Stability Analysis of Delaunay Surfaces as Steady States for the Surface Diffusion Equation. In: Gazzola, F., Ishige, K., Nitsch, C., Salani, P. (eds) Geometric Properties for Parabolic and Elliptic PDE's. GPPEPDEs 2015. Springer Proceedings in Mathematics & Statistics, vol 176. Springer, Cham. https://doi.org/10.1007/978-3-319-41538-3_8

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