Open AccessSupport properties of solutions to nonlinear parabolic equations with variable density in the hyperbolic space
Author(s) -
Fabio Punzo
Publication year - 2012
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2012.5.657
Subject(s) - mathematics , geodetic datum , infinity , nonlinear system , mathematical analysis , space (punctuation) , variable (mathematics) , initial value problem , cauchy problem , hyperbolic partial differential equation , simple (philosophy) , hyperbolic space , cauchy distribution , partial differential equation , physics , computer science , philosophy , cartography , epistemology , quantum mechanics , geography , operating system
We consider the Cauchy problem for a class of nonlinear parabolic equations with variable density in the hyperbolic space, assuming that the initial datum has compact support. We provide simple conditions, involving the behaviour of the density at infinity, so that the support of every nonnegative solution is not compact at some positive time, or it remains compact for any positive time. These results extend to the case of the hyperbolic space those given in [8] for the Cauchy problem in IRn