On the mixed problem for hyperbolic partial differential-functional equations of the first order

Tomasz Człapiński

Czechoslovak Mathematical Journal (1999)

  • Volume: 49, Issue: 4, page 791-809
  • ISSN: 0011-4642

Abstract

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We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order D x z ( x , y ) = f ( x , y , z ( x , y ) , D y z ( x , y ) ) , where z ( x , y ) [ - τ , 0 ] × [ 0 , h ] → ℝ is a function defined by z ( x , y ) ( t , s ) = z ( x + t , y + s ) , ( t , s ) ∈ [ - τ , 0 ] × [ 0 , h ] . Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem.

How to cite

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Człapiński, Tomasz. "On the mixed problem for hyperbolic partial differential-functional equations of the first order." Czechoslovak Mathematical Journal 49.4 (1999): 791-809. <http://eudml.org/doc/30523>.

@article{Człapiński1999,
abstract = {We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order \[ D\_xz(x,y) = f(x,y,z\_\{(x,y)\}, D\_yz(x,y)), \] where $z_\{(x,y)\} \: [-\tau ,0] \times [0,h] \rightarrow \mathbb \{R\}$ is a function defined by $z_\{(x,y)\}(t,s) = z(x+t, y+s)$, $(t,s) \in [-\tau ,0] \times [0,h]$. Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem.},
author = {Człapiński, Tomasz},
journal = {Czechoslovak Mathematical Journal},
keywords = {partial differential-functional equations; mixed problem; generalized solutions; local existence; bicharacteristics; successive approximations; generalized solutions; local existence; bicharacteristics; successive approximations},
language = {eng},
number = {4},
pages = {791-809},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the mixed problem for hyperbolic partial differential-functional equations of the first order},
url = {http://eudml.org/doc/30523},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Człapiński, Tomasz
TI - On the mixed problem for hyperbolic partial differential-functional equations of the first order
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 4
SP - 791
EP - 809
AB - We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order \[ D_xz(x,y) = f(x,y,z_{(x,y)}, D_yz(x,y)), \] where $z_{(x,y)} \: [-\tau ,0] \times [0,h] \rightarrow \mathbb {R}$ is a function defined by $z_{(x,y)}(t,s) = z(x+t, y+s)$, $(t,s) \in [-\tau ,0] \times [0,h]$. Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem.
LA - eng
KW - partial differential-functional equations; mixed problem; generalized solutions; local existence; bicharacteristics; successive approximations; generalized solutions; local existence; bicharacteristics; successive approximations
UR - http://eudml.org/doc/30523
ER -

References

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