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Support properties of solutions to nonlinear parabolic equations with variable density in the hyperbolic space. (English) Zbl 1251.35040

Summary: 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 [S. Kamin and R. Kersner, Meccanica 28, No. 2, 117–120 (1993; Zbl 0786.76088)] for the Cauchy problem in \(\mathbb{R}^n\).

MSC:

35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations
35K67 Singular parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35B51 Comparison principles in context of PDEs

Citations:

Zbl 0786.76088
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