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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Language to use for this widget.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Number of notes per page

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.