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A note on surfaces with radially symmetric nonpositive Gaussian curvature

Joseph Shomberg (2005)

Mathematica Bohemica

It is easily seen that the graphs of harmonic conjugate functions (the real and imaginary parts of a holomorphic function) have the same nonpositive Gaussian curvature. The converse to this statement is not as simple. Given two graphs with the same nonpositive Gaussian curvature, when can we conclude that the functions generating their graphs are harmonic? In this paper, we show that given a graph with radially symmetric nonpositive Gaussian curvature in a certain form, there are (up to) four families...

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

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

Mathematica Bohemica

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).

A note on the generalized energy inequality in the Navier-Stokes equations

Petr Kučera, Zdeněk Skalák (2003)

Applications of Mathematics

We prove that there exists a suitable weak solution of the Navier-Stokes equation, which satisfies the generalized energy inequality for every nonnegative test function. This improves the famous result on existence of a suitable weak solution which satisfies this inequality for smooth nonnegative test functions with compact support in the space-time.

A note on the paper of Y. Naito

Piotr Biler (2006)

Banach Center Publications

This note contains some remarks on the paper of Y. Naito concerning the parabolic system of chemotaxis and published in this volume.

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