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

Commentationes Mathematicae (2008)

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

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topAdrian 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 -

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