Displaying similar documents to “Growth and accretion of mass in an astrophysical model”

On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions

Théodore K. Boni (1999)

Commentationes Mathematicae Universitatis Carolinae

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We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions tend to zero or blow up in a finite time. We also give the asymptotic behavior of solutions which tend to zero as t → ∞ . Finally, we obtain the asymptotic behavior near the blow-up time of certain blow-up solutions and describe their blow-up set.

Global solutions via partial information and the Cahn-Hilliard equation

Jan Cholewa, Tomasz Dłotko (1996)

Banach Center Publications

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Global solutions of semilinear parabolic equations are studied in the case when some weak a priori estimate for solutions of the problem under consideration is already known. The focus is on the rapid growth of the nonlinear term for which existence of the semigroup and certain dynamic properties of the considered system can be justified. Examples including the famous Cahn-Hilliard equation are finally discussed.