Displaying similar documents to “Pseudodifferential parametrices of infinite order for SG-hyperbolic problems.”

General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations

N. Dilna, A. Rontó (2008)

Mathematica Bohemica

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New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.

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).