# The method of quasilinearization for system of hyperbolic functional differential equations

• Volume: 48, Issue: 2
• ISSN: 2080-1211

top Access to full text Full (PDF)

## Abstract

top
We deal with monotone iterative method for the Darboux problem for the system of hyperbolic partial functional-differential equations $\left\{\begin{array}{c}\frac{{\partial }^{2}u}{\partial x\partial y}\left(x,y\right)=f\left(x,y,{u}_{\left(x,y\right)},{u}_{\left(x,y\right)},\text{a.e.}\phantom{\rule{4.0pt}{0ex}}\text{in}\phantom{\rule{4pt}{0ex}}\left[0,1\right]×\left[0,b\right]\hfill \\ u\left(x,y\right)=\psi \left(x,y\right),\text{on}\phantom{\rule{4pt}{0ex}}\left[-{a}_{0},a\right]×\left[-{b}_{0},b\right]\setminus \left(0,a\right]×\left(0,b\right],\hfill \end{array}\right\$ where the function ${u}_{\left(x,y\right)}:\left[-{a}_{0},0\right]×\left[-{b}_{0},0\right]\to {ℝ}^{k}$ is defined by ${u}_{\left(x,y\right)}\left(s,t\right)=u\left(s+x,t+y\right)$ for $\left(s,t\right)\in \left[-{a}_{0},0\right]×\left[-{b}_{0},0\right]$.

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

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

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.