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Generic hyperbolicity for reaction diffusion equations on symmetric domains

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Summary

The problem of generic hyperbolicity for reaction diffusion equations with Dirichlet boundary conditions on a ball inR n is studied. It is proved that while hyperbolicity is not a generic property, radially symmetric solutions are generically hyperbolic.

Zusammenfassung

Das Problem der generischen Hyperbolizität für Reaktion-Diffusionsgleichungen mit Dirichletschen Randbedingungen in einer Kugel imR n wird betrachtet. Es wird bewiesen, daß radialsymmetrische Lösungen generisch symmetrische sind, während Hyperbolizität nicht eine generische Eigenschaft ist.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Comenius University, 84215, Mlynská dolina, Bratislava, Czechoslovakia

    Pavol Brunovský & Peter Poláčik

Authors
  1. Pavol Brunovský
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  2. Peter Poláčik
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Brunovský, P., Poláčik, P. Generic hyperbolicity for reaction diffusion equations on symmetric domains. Z. angew. Math. Phys. 38, 172–183 (1987). https://doi.org/10.1007/BF00945403

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  • DOI: https://doi.org/10.1007/BF00945403

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