Front propagation for nonlinear diffusion equations on the hyperbolic space
Hiroshi Matano, Fabio Punzo, Alberto Tesei
Source abstract
We study the Cauchy problem in the hyperbolic space \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 \mathbb R^n new phenomena arise, which depend on the properties of the diffusion process in \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 \mathbb R^n .
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