Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation

Dariusz Idczak

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 1, page 145-171
  • ISSN: 0011-4642

Abstract

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We give characterizations of the distributional derivatives D 1 , 1 , D 1 , 0 , D 0 , 1 of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.

How to cite

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Idczak, Dariusz. "Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation." Czechoslovak Mathematical Journal 48.1 (1998): 145-171. <http://eudml.org/doc/30409>.

@article{Idczak1998,
abstract = {We give characterizations of the distributional derivatives $D^\{1,1\}$, $D^\{1,0\}$, $D^\{0,1\}$ of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.},
author = {Idczak, Dariusz},
journal = {Czechoslovak Mathematical Journal},
keywords = {distributional derivatives; locally finite variation; impulsive hyperbolic equation},
language = {eng},
number = {1},
pages = {145-171},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation},
url = {http://eudml.org/doc/30409},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Idczak, Dariusz
TI - Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 1
SP - 145
EP - 171
AB - We give characterizations of the distributional derivatives $D^{1,1}$, $D^{1,0}$, $D^{0,1}$ of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.
LA - eng
KW - distributional derivatives; locally finite variation; impulsive hyperbolic equation
UR - http://eudml.org/doc/30409
ER -

References

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