The method of quasilinearization for system of hyperbolic functional differential equations

Adrian Karpowicz

Commentationes Mathematicae, Tome 48 (2008) no. 2, pp. 155-168.

Résumé

We deal with monotone iterative method for the Darboux problem for the system of hyperbolic partial functional-differential equations \[ \begin{cases} \frac{\partial^2 u}{\partial x\partial y} (x,y) = f(x,y,u_{(x,y)}, u_{(x,y)}, \text{a.e. in}\ [0,1]\times [0,b]\\ u(x,y) = \psi (x,y), \text{on}\ [-a_0,a]\times [-b_0,b] \setminus (0,a] \times (0,b], \end{cases} \] where the function \(u_{(x,y)}\colon [-a_0,0]\times [-b_0,0] \to \mathbb{R}^k\) is defined by \(u_{(x,y)} (s, t) = u(s + x, t + y)\) for \((s, t)\in [-a_0 , 0] \times [-b_0 , 0]\).

Détail

DOI : 10.14708/cm.v48i2.5269

Mots-clés : Monotone iterative technique, Generalized quasilinearization, Hyperbolic equations, Darboux problem, Functional differential inequalities