On the mixed problem for quasilinear partial functional differential equations with unbounded delay

Człapiński, Tomasz. "On the mixed problem for quasilinear partial functional differential equations with unbounded delay." Annales Polonici Mathematici 72.1 (1999): 87-98. <http://eudml.org/doc/262827>.

@article{Człapiński1999,
abstract = {We consider the mixed problem for the quasilinear partial functional differential equation with unbounded delay $D_tz(t,x) = ∑_\{i=1\}^n f_i(t,x,z_\{(t,x)\})D_\{x_i\}z(t,x) + h(t,x,z_\{(t,x)\})$, where $z_\{(t,x)\} ∈ X̶_0$ is defined by $z_\{(t,x)\}(τ,s) = z(t+τ,x+s)$, $(τ,s) ∈ (-∞,0]×[0,r]$, and the phase space $X̶_0$ satisfies suitable axioms. Using the method of bicharacteristics and the fixed-point method we prove a theorem on the local existence and uniqueness of Carathéodory solutions of the mixed problem.},
author = {Człapiński, Tomasz},
journal = {Annales Polonici Mathematici},
keywords = {Carathéodory solutions; functional differential equation; bicharacteristics; fixed-point theorem; mixed problem; unbounded delay; fixed-point method; local existence and uniqueness of Carathéodory solutions},
language = {eng},
number = {1},
pages = {87-98},
title = {On the mixed problem for quasilinear partial functional differential equations with unbounded delay},
url = {http://eudml.org/doc/262827},
volume = {72},
year = {1999},
}

TY - JOUR
AU - Człapiński, Tomasz
TI - On the mixed problem for quasilinear partial functional differential equations with unbounded delay
JO - Annales Polonici Mathematici
PY - 1999
VL - 72
IS - 1
SP - 87
EP - 98
AB - We consider the mixed problem for the quasilinear partial functional differential equation with unbounded delay $D_tz(t,x) = ∑_{i=1}^n f_i(t,x,z_{(t,x)})D_{x_i}z(t,x) + h(t,x,z_{(t,x)})$, where $z_{(t,x)} ∈ X̶_0$ is defined by $z_{(t,x)}(τ,s) = z(t+τ,x+s)$, $(τ,s) ∈ (-∞,0]×[0,r]$, and the phase space $X̶_0$ satisfies suitable axioms. Using the method of bicharacteristics and the fixed-point method we prove a theorem on the local existence and uniqueness of Carathéodory solutions of the mixed problem.
LA - eng
KW - Carathéodory solutions; functional differential equation; bicharacteristics; fixed-point theorem; mixed problem; unbounded delay; fixed-point method; local existence and uniqueness of Carathéodory solutions
UR - http://eudml.org/doc/262827
ER -