Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2006-09-30
Associated Spaces Defined by Ordinary Differential EquationsLe Thu Hoai and Wolfgang Tutschke (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