# Front propagation for nonlinear diffusion equations on the hyperbolic space

Hiroshi Matano; Fabio Punzo; Alberto Tesei

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 5, page 1199-1227
- ISSN: 1435-9855

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topMatano, 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 -

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