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Zeitschrift für Analysis und ihre Anwendungen

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Volume 25, Issue 3, 2006, pp. 385–392
DOI: 10.4171/ZAA/1295

Published online: 2006-09-30

Associated Spaces Defined by Ordinary Differential Equations

Le Thu Hoai[1] and Wolfgang Tutschke[2]

(1) Faculty of Applied Mathematics and Informatics, Hanoi, Vietnam
(2) Technische Universität Graz, Austria

The paper deals with initial value problems for desired functions $u(t,x)$ depending on the time $t$ and one spacelike variable $x$. In case the initial function $\varphi (x)$ satisfies an associated (ordinary) differential equation, the solution $u(t,x)$ satisfies the associated differential equation for each $t$. If the general solution of the associated differential equation is known, one gets a system of ordinary differential equations for the desired coefficients depending on $t$. In any case, the solution can be obtained as fixed point of a related integro-differential operator.

Keywords: Initial value problem, contraction-mapping principle, separation of variables, conservation law

Hoai Le Thu, Tutschke Wolfgang: Associated Spaces Defined by Ordinary Differential Equations. Z. Anal. Anwend. 25 (2006), 385-392. doi: 10.4171/ZAA/1295