On periodic in the plane solutions of second order linear hyperbolic systems

Tariel Kiguradze

Archivum Mathematicum (1997)

  • Volume: 033, Issue: 4, page 253-272
  • ISSN: 0044-8753

Abstract

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Sufficient conditions for the problem ∂ 2 u ∂ x ∂ y = P 0 ( x , y ) u + P 1 ( x , y ) ∂ u ∂ x + P 2 ( x , y ) ∂ u ∂ y + q ( x , y ) , u ( x + ω 1 , y ) = u ( x , y ) , u ( x , y + ω 2 ) = u ( x , y ) to have the Fredholm property and to be uniquely solvable are established, where ω 1 and ω 2 are positive constants and P j : R 2 → R n × n ( j = 0 , 1 , 2 ) and q : R 2 → R n are continuous matrix and vector functions periodic in x and y .

How to cite

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Kiguradze, Tariel. "On periodic in the plane solutions of second order linear hyperbolic systems." Archivum Mathematicum 033.4 (1997): 253-272. <http://eudml.org/doc/248019>.

@article{Kiguradze1997,
abstract = {Sufficient conditions for the problem \[ \{\partial ^2 u\over \partial x\partial y\}=P\_0(x,y)u+ P\_1(x,y)\{\partial u\over \partial x\}+P\_2(x,y)\{\partial u\over \partial y\}+ q(x,y), u(x+\omega \_1,y)=u(x,y),\quad u(x,y+\omega \_2)=u(x,y) \] to have the Fredholm property and to be uniquely solvable are established, where $\omega _1$ and $\omega _2$ are positive constants and $P_j:R^2\rightarrow R^\{n\times n\}$$(j=0,1,2)$ and $q:R^2\rightarrow R^n$ are continuous matrix and vector functions periodic in $x$ and $y$.},
author = {Kiguradze, Tariel},
journal = {Archivum Mathematicum},
keywords = {hyperbolic system; periodic solution; F property; Fredholm property},
language = {eng},
number = {4},
pages = {253-272},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On periodic in the plane solutions of second order linear hyperbolic systems},
url = {http://eudml.org/doc/248019},
volume = {033},
year = {1997},
}

TY - JOUR
AU - Kiguradze, Tariel
TI - On periodic in the plane solutions of second order linear hyperbolic systems
JO - Archivum Mathematicum
PY - 1997
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 033
IS - 4
SP - 253
EP - 272
AB - Sufficient conditions for the problem \[ {\partial ^2 u\over \partial x\partial y}=P_0(x,y)u+ P_1(x,y){\partial u\over \partial x}+P_2(x,y){\partial u\over \partial y}+ q(x,y), u(x+\omega _1,y)=u(x,y),\quad u(x,y+\omega _2)=u(x,y) \] to have the Fredholm property and to be uniquely solvable are established, where $\omega _1$ and $\omega _2$ are positive constants and $P_j:R^2\rightarrow R^{n\times n}$$(j=0,1,2)$ and $q:R^2\rightarrow R^n$ are continuous matrix and vector functions periodic in $x$ and $y$.
LA - eng
KW - hyperbolic system; periodic solution; F property; Fredholm property
UR - http://eudml.org/doc/248019
ER -

References

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