Displaying similar documents to “Existence and nonexistence of solutions for a model of gravitational interaction of particles, III”

Growth and accretion of mass in an astrophysical model

Piotr Biler (1995)

Applicationes Mathematicae

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We study asymptotic behavior of radial solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles. In particular, we consider stationary solutions in balls and in the whole space, self-similar solutions defined globally in time, blowing up self-similar solutions, and singularities of solutions that blow up in a finite time.

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.

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.

Abstract parabolic problem with non-Lipschitz nonlinearity

Jan Cholewa, Tomasz Dlotko (2000)

Banach Center Publications

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An abstract parabolic equation with sectorial operator and continuous nonlinearity is studied in this paper. In particular, the asymptotic behavior of solutions is described within the framework of the theory of global attractors. Examples included in the final part of the paper illustrate the presented ideas.