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

Irina Kmit

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 4, page 631-645
  • ISSN: 0010-2628

Abstract

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We study one-dimensional linear hyperbolic systems with L ∞ -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.

How to cite

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Kmit, Irina. "Linear hyperbolic problems in the whole scale of Sobolev-type spaces of periodic functions." Commentationes Mathematicae Universitatis Carolinae 48.4 (2007): 631-645. <http://eudml.org/doc/250187>.

@article{Kmit2007,
abstract = {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.},
author = {Kmit, Irina},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {hyperbolic systems; periodic-Dirichlet problems; anisotropic Sobolev spaces; a priori estimates; 1D linear hyperbolic systems; periodic solutions},
language = {eng},
number = {4},
pages = {631-645},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Linear hyperbolic problems in the whole scale of Sobolev-type spaces of periodic functions},
url = {http://eudml.org/doc/250187},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Kmit, Irina
TI - Linear hyperbolic problems in the whole scale of Sobolev-type spaces of periodic functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 4
SP - 631
EP - 645
AB - 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.
LA - eng
KW - hyperbolic systems; periodic-Dirichlet problems; anisotropic Sobolev spaces; a priori estimates; 1D linear hyperbolic systems; periodic solutions
UR - http://eudml.org/doc/250187
ER -

References

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