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$C^{1}$ -smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions

Irina Kmit — 2011

Commentationes Mathematicae Universitatis Carolinae

We consider a class of Nemytskii superposition operators that covers the nonlinear part of traveling wave models from laser dynamics, population dynamics, and chemical kinetics. Our main result is the $C^{1}$ -continuity property of these operators over Sobolev-type spaces of periodic functions.

Linear hyperbolic problems in the whole scale of Sobolev-type spaces of periodic functions

Irina Kmit — 2007

Commentationes Mathematicae Universitatis Carolinae

We study one-dimensional linear hyperbolic systems with $L^{\infty}$ -coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of solutions in the whole scale of Sobolev-type spaces of periodic functions. These spaces give an optimal regularity trade-off for our problem.

Generalized solutions to singular initial-boundary hyperbolic problems with non-lipshitz nonlinearities

Irina Kmit — 2006

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

A distributional solution to a hyperbolic problem arising in population dynamics.

Kmit, Irina — 2007

Electronic Journal of Differential Equations (EJDE) [electronic only]

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