Sets of determination for parabolic functions on a half-space

Jarmila Ranošová

Displaying similar documents to “Sets of determination for parabolic functions on a half-space”

Characterization of sets of determination for parabolic functions on a slab by coparabolic (minimal) thinness

Jarmila Ranošová (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let $T$ be a positive number or $+ \infty$ . We characterize all subsets $M$ of $ℝ^{n} \times] 0, T [$ such that $inf_{X \in ℝ^{n} \times] 0, T [} u (X) = inf_{X \in M} u (X) i$ for every positive parabolic function $u$ on $ℝ^{n} \times] 0, T [$ in terms of coparabolic (minimal) thinness of the set $M_{δ} = \cup_{(x, t) \in M} B^{p} ((x, t), δ t)$ , where $δ \in (0, 1)$ and $B^{p} ((x, t), r)$ is the “heat ball” with the “center” $(x, t)$ and radius $r$ . Examples of different types of sets which can be used instead of “heat balls” are given. It is proved that (i) is equivalent to the condition ${sup}_{X \in ℝ^{n} \times ℝ^{+}} u (X) = {sup}_{X \in M} u (X)$ for every bounded parabolic function on $ℝ^{n} \times ℝ^{+}$ and hence to all equivalent conditions given in the article...

Existence and asymptotic behaviour of positive solutions for some nonlinear parabolic systems in the half-space.

Ghanmi, Abdeljabbar, Toumi, Faten (2011)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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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 $| u | \to \infty$ 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).