The method of quasilinearization for system of hyperbolic functional differential equations

Adrian Karpowicz. "The method of quasilinearization for system of hyperbolic functional differential equations." Commentationes Mathematicae 48.2 (2008): null. <http://eudml.org/doc/292043>.

@article{AdrianKarpowicz2008,
abstract = {We deal with monotone iterative method for the Darboux problem for the system of hyperbolic partial functional-differential equations \[ \{\left\lbrace \begin\{array\}\{ll\} \frac\{\partial ^2 u\}\{\partial x\partial y\} (x,y) = f(x,y,u\_\{(x,y)\}, u\_\{(x,y)\}, \text\{a.e. in\}\ [0,1]\times [0,b]\\ u(x,y) = \psi (x,y), \text\{on\}\ [-a\_0,a]\times [-b\_0,b] \setminus (0,a] \times (0,b], \end\{array\}\right.\} \] where the function $u_\{(x,y)\}\colon [-a_0,0]\times [-b_0,0] \rightarrow \mathbb \{R\}^k$ is defined by $u_\{(x,y)\} (s, t) = u(s + x, t + y)$ for $(s, t)\in [-a_0 , 0] \times [-b_0 , 0]$.},
author = {Adrian Karpowicz},
journal = {Commentationes Mathematicae},
keywords = {Monotone iterative technique; Generalized quasilinearization; Hyperbolic equations; Darboux problem; Functional differential inequalities},
language = {eng},
number = {2},
pages = {null},
title = {The method of quasilinearization for system of hyperbolic functional differential equations},
url = {http://eudml.org/doc/292043},
volume = {48},
year = {2008},
}

TY - JOUR
AU - Adrian Karpowicz
TI - The method of quasilinearization for system of hyperbolic functional differential equations
JO - Commentationes Mathematicae
PY - 2008
VL - 48
IS - 2
SP - null
AB - We deal with monotone iterative method for the Darboux problem for the system of hyperbolic partial functional-differential equations \[ {\left\lbrace \begin{array}{ll} \frac{\partial ^2 u}{\partial x\partial y} (x,y) = f(x,y,u_{(x,y)}, u_{(x,y)}, \text{a.e. in}\ [0,1]\times [0,b]\\ u(x,y) = \psi (x,y), \text{on}\ [-a_0,a]\times [-b_0,b] \setminus (0,a] \times (0,b], \end{array}\right.} \] where the function $u_{(x,y)}\colon [-a_0,0]\times [-b_0,0] \rightarrow \mathbb {R}^k$ is defined by $u_{(x,y)} (s, t) = u(s + x, t + y)$ for $(s, t)\in [-a_0 , 0] \times [-b_0 , 0]$.
LA - eng
KW - Monotone iterative technique; Generalized quasilinearization; Hyperbolic equations; Darboux problem; Functional differential inequalities
UR - http://eudml.org/doc/292043
ER -