Displaying similar documents to “Characterization of sets of determination for parabolic functions on a slab by coparabolic (minimal) thinness”

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 n × + such that sup X n × + u ( X ) = sup X M u ( X ) for every bounded parabolic function u on n × + . 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. ...

Large time behavior of solutions to a class of doubly nonlinear parabolic equations

Hua Shui Zhan (2008)

Applications of Mathematics

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We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation u t = div ( u m - 1 | D u | p - 2 D u ) - u q with an initial condition u ( x , 0 ) = u 0 ( x ) . Here the exponents m , p and q satisfy m + p 3 , p > 1 and q > m + p - 2 .

A note on the Cahn-Hilliard equation in H 1 ( 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 ( 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 ( 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).