Mathematical Sciences: Volterra Integral Equations in Abstract Spaces

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Work to be done on this project concerns several related problems concerning Volterra integrodifferential equations in Banach spaces. Applications are planned to partial differential integral equations of the type occurring in the modeling of viscoelastic media and associated control problems. The work builds on earlier investigations and involves semigroups, cosine families and the related theory. Emphasis will be placed on finding appropriate settings and models which will yield qualitative information which can conveniently be applied. Specific problems to be analyzed include the examination of equations in Banach spaces which depend on data that incorporate all past history. The role of one of these equations representing the limiting equation for equations which do not depend on the full past history will be considered. A semigroup formulation for certain infinite history problems developed earlier will continue to receive attention. Work on symmetric hyperbolic systems will also be continued. The connecting theme in this effort is that of boundary control.