We investigate the well-posedness of the Cauchy problem for a class of nonlinear parabolic equations with variable density in the hyperbolic space. We state sufficient conditions for uniqueness or nonuniqueness of bounded solutions, depending on the behavior of the density at infinity. Nonuniqueness relies on the prescription at infinity of suitable conditions of Dirichlet type, and possibly inhomogeneous. © 2011 Springer Basel AG.

Well-posedness of the Cauchy problem for nonlinear parabolic equations with variable density in the hyperbolic space

PUNZO, FABIO
2012-01-01

Abstract

We investigate the well-posedness of the Cauchy problem for a class of nonlinear parabolic equations with variable density in the hyperbolic space. We state sufficient conditions for uniqueness or nonuniqueness of bounded solutions, depending on the behavior of the density at infinity. Nonuniqueness relies on the prescription at infinity of suitable conditions of Dirichlet type, and possibly inhomogeneous. © 2011 Springer Basel AG.
2012
Comparison principles; Laplace-Beltramioperator; Singular nonlinear parabolic equations; Sub-supersolutions; Well-posedness; Analysis; Applied Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1028577
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