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Bifurcation from Symmetry

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Nonlinear Diffusion Equations and Their Equilibrium States II

Part of the book series: Mathematical Sciences Research Institute Publications ((MSRI,volume 13))

Abstract

In this report, we announce several new results concerning the existence of non-symmetric solutions of symmetric equations (complete details of the proofs can be found in [7]). Our approach to this question is through bifurcation theory whereby we shall obtain the asymmetric solutions from symmetric ones via a bifurcation procedure.

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References

  1. G. Cerami, Symmetry breaking for a class of semüinear elliptic equations, Nonlinear Anal. 10 (1986), 1–14.

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  2. E. N. Dancer, On non-radially symmetric bifurcation, J. London Math. Soc. 20 (1979), 287–292.

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  3. K. T. Smith, “Primer of Modern Analysis,” UTM (Springer), 1983.

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  4. J. A. Smoller, “Shock Waves and Reaction-Diffusion Equations,” Grundlehren (Springer), 1983.

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  5. J. A. Smoller and A. Wasserman, Symmetry-breaking for positive solutions of semilinear elliptic equations, Arch. Rat. Mech. Anal. 95 (1986), 217–225.

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  6. J. A. Smoller and A. Wasserman, Symmetry-breaking for semilinear elliptic equations with general boundary conditions, Comm. Math. Phys. 105 (1986), 415–441.

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  7. J. A. Smoller and A. Wasserman, Symmetry, degeneracy and universality in semilinear elliptic equations, to appear.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    J. Smoller & A. G. Wasserman

Authors
  1. J. Smoller
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  2. A. G. Wasserman
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    W.-M. Ni  & James Serrin  & 

  2. Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA, 94720, USA

    W.-M. Ni  & James Serrin  & 

  3. Department of Mathematics and Computer Science, University of Leiden, The Netherlands

    L. A. Peletier

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© 1988 Springer-Verlag New York Inc.

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Smoller, J., Wasserman, A.G. (1988). Bifurcation from Symmetry. In: Ni, WM., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States II. Mathematical Sciences Research Institute Publications, vol 13. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9608-6_16

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  • DOI: https://doi.org/10.1007/978-1-4613-9608-6_16

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9610-9

  • Online ISBN: 978-1-4613-9608-6

  • eBook Packages: Springer Book Archive

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