Front propagation for nonlinear diffusion equations on the hyperbolic space

Matano, Hiroshi, Punzo, Fabio, and Tesei, Alberto. "Front propagation for nonlinear diffusion equations on the hyperbolic space." Journal of the European Mathematical Society 017.5 (2015): 1199-1227. <http://eudml.org/doc/277707>.

@article{Matano2015,
abstract = {We study the Cauchy problem in the hyperbolic space $\mathbb \{H\}^n (n\ge 2)$ 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 $\mathbb \{R\}^n$ 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 $\mathbb \{R\}^n$.},
author = {Matano, Hiroshi, Punzo, Fabio, Tesei, Alberto},
journal = {Journal of the European Mathematical Society},
keywords = {semilinear parabolic equations; hyperbolic space; extinction and propagation; asymptotical symmetry of solutions; horospheric waves; Kolmogorov-Petrovskii-Piskunov equation; Allen-Cahn equation; critical velocity; Fujita exponent; Kolmogorov-Petrovskii-Piskunov equation; Allen-Cahn equation; critical velocity; extinction; Fujita exponent},
language = {eng},
number = {5},
pages = {1199-1227},
publisher = {European Mathematical Society Publishing House},
title = {Front propagation for nonlinear diffusion equations on the hyperbolic space},
url = {http://eudml.org/doc/277707},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Matano, Hiroshi
AU - Punzo, Fabio
AU - Tesei, Alberto
TI - Front propagation for nonlinear diffusion equations on the hyperbolic space
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 5
SP - 1199
EP - 1227
AB - We study the Cauchy problem in the hyperbolic space $\mathbb {H}^n (n\ge 2)$ 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 $\mathbb {R}^n$ 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 $\mathbb {R}^n$.
LA - eng
KW - semilinear parabolic equations; hyperbolic space; extinction and propagation; asymptotical symmetry of solutions; horospheric waves; Kolmogorov-Petrovskii-Piskunov equation; Allen-Cahn equation; critical velocity; Fujita exponent; Kolmogorov-Petrovskii-Piskunov equation; Allen-Cahn equation; critical velocity; extinction; Fujita exponent
UR - http://eudml.org/doc/277707
ER -