Perturbative methods in scales of Banach spaces: applications for Gevrey regularity of solutions to semilinear partial differential equations.

Gramchev, T.

Displaying similar documents to “Perturbative methods in scales of Banach spaces: applications for Gevrey regularity of solutions to semilinear partial differential equations.”

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Regularity of weakly well-posed characteristic boundary value problems.

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Decay for travelling waves in the Gross–Pitaevskii equation

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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).