JournalszaaVol. 25 , No. 3DOI 10.4171/zaa/1295

Associated Spaces Defined by Ordinary Differential Equations

  • Wolfgang Tutschke

    Technische Universität Graz, Austria
  • Le Thu Hoai

    Faculty of Applied Mathematics and Informatics, Hanoi, Vietnam
Associated Spaces Defined by Ordinary Differential Equations cover

Abstract

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