JournalsjemsVol. 17 , No. 5pp. 1199–1227

Front propagation for nonlinear diffusion equations on the hyperbolic space

  • Hiroshi Matano

    University of Tokyo, Japan
  • Fabio Punzo

    Università degli Studi di Milano, Italy
  • Alberto Tesei

    Università di Roma La Sapienza, Italy
Front propagation for nonlinear diffusion equations on the hyperbolic space cover
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Abstract

We study the Cauchy problem in the hyperbolic space Hn(n2)\mathbb{H}^n (n\ge2) for the semilinear heat equation with forcing term, which is either of KPP type or of Allen-Cahn type. Propagation and extinction of solutions, asymptotical speed of propagation and asymptotical symmetry of solutions are addressed. With respect to the corresponding problem in the Euclidean space Rn\mathbb R^n new phenomena arise, which depend on the properties of the diffusion process in Hn\mathbb{H}^n. We also investigate a family of travelling wave solutions, named horospheric waves, which have properties similar to those of plane waves in Rn\mathbb R^n.

Cite this article

Hiroshi Matano, Fabio Punzo, Alberto Tesei, Front propagation for nonlinear diffusion equations on the hyperbolic space. J. Eur. Math. Soc. 17 (2015), no. 5 pp. 1199–1227

DOI 10.4171/JEMS/529