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

Czechoslovak Mathematical Journal (1998)

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

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topIdczak, 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 -

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