# American Institute of Mathematical Sciences

June  2012, 5(3): 657-670. doi: 10.3934/dcdss.2012.5.657

## Support properties of solutions to nonlinear parabolic equations with variable density in the hyperbolic space

 1 Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P.le A. Moro 5, I-00185 Roma

Received  June 2010 Revised  August 2010 Published  October 2011

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 $\mathbb{R}^n$.
Citation: Fabio Punzo. Support properties of solutions to nonlinear parabolic equations with variable density in the hyperbolic space. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 657-670. doi: 10.3934/dcdss.2012.5.657
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