Geodesic
Front propagation for nonlinear diffusion equations on the hyperbolic space
Journal of the European Mathematical Society, Tome 17 (2015) no. 5, pp. 1199-1227 Cet article a éte moissonné depuis la source EMS Press

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We study the Cauchy problem in the hyperbolic space Hn(n≥2) 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 new phenomena arise, which depend on the properties of the diffusion process in Hn. We also investigate a family of travelling wave solutions, named horospheric waves, which have properties similar to those of plane waves in Rn.
DOI : 10.4171/jems/529
Classification : 35-XX
Keywords: Semilinear parabolic equations, hyperbolic space, extinction and propagation, asymptotical symmetry of solutions, horospheric waves 
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     author = {Hiroshi Matano and Fabio Punzo and Alberto Tesei},
     title = {Front propagation for nonlinear diffusion equations on the hyperbolic space},
     journal = {Journal of the European Mathematical Society},
     pages = {1199--1227},
     year = {2015},
     volume = {17},
     number = {5},
     doi = {10.4171/jems/529},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/529/}
}
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Hiroshi Matano; Fabio Punzo; Alberto Tesei. Front propagation for nonlinear diffusion equations on the hyperbolic space. Journal of the European Mathematical Society, Tome 17 (2015) no. 5, pp. 1199-1227. doi: 10.4171/jems/529

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