Displaying similar documents to “Existence and asymptotic behaviour of positive solutions for some nonlinear parabolic systems in the half-space.”

A note on the Cahn-Hilliard equation in H 1 ( ℝ N ) involving critical exponent

Jan W. Cholewa, Aníbal Rodríguez-Bernal (2014)

Mathematica Bohemica

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We consider the Cahn-Hilliard equation in H 1 ( ℝ N ) with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as | u | → ∞ and logistic type nonlinearities. In both situations we prove the H 2 ( ℝ N ) -bound on the solutions and show that the individual solutions are suitably attracted by the set of equilibria. This complements the results in the literature; see J. W. Cholewa, A. Rodriguez-Bernal (2012).

Sets of determination for parabolic functions on a half-space

Jarmila Ranošová (1994)

Commentationes Mathematicae Universitatis Carolinae

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We characterize all subsets M of ℝ n × ℝ + such that sup X ∈ ℝ n × ℝ + u ( X ) = sup X ∈ M u ( X ) for every bounded parabolic function u on ℝ n × ℝ + . The closely related problem of representing functions as sums of Weierstrass kernels corresponding to points of M is also considered. The results provide a parabolic counterpart to results for classical harmonic functions in a ball, see References. As a by-product the question of representability of probability continuous distributions as sums of multiples of normal distributions is investigated. ...