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

Czechoslovak Mathematical Journal (1999)

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

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topCzłapiński, 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 -

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