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dc.contributor.authorBaker, Christopher T. H.*
dc.contributor.authorLumb, Patricia M.*
dc.date.accessioned2015-03-13T13:19:01Z
dc.date.available2015-03-13T13:19:01Z
dc.date.issued2006
dc.identifier.citationChester : University of Chester, 2006en
dc.identifier.urihttp://hdl.handle.net/10034/346601
dc.description.abstractIn discussions of certain neutral delay differential equations in Hale’s form, the relationship of the original problem with an integrated form (an integral equation) proves to be helpful in considering existence and uniqueness of a solution and sensitivity to initial data. Although the theory is generally based on the assumption that a solution is continuous, natural solutions of neutral delay differential equations of the type considered may be discontinuous. This difficulty is resolved by relating the discontinuous solution to its restrictions on appropriate (half-open) subintervals where they are continuous and can be regarded as solutions of related integral equations. Existence and unicity theories then follow. Furthermore, it is seen that the discontinuous solutions can be regarded as solutions in the sense of Caratheodory (where this concept is adapted from the theory of ordinary differential equations, recast as integral equations).
dc.language.isoenen
dc.publisherUniversity of Chesteren
dc.relation.ispartofseriesApplied Mathematics Group Research Reporten
dc.relation.ispartofseries2006 : 2en
dc.relation.urlhttp://www.chester.ac.uken
dc.subjectexistence theoryen
dc.subjectevolutionary equationsen
dc.subjectintegral equationsen
dc.titleExistence theory for a class of evolutionary equations with time-lag, studied via integral equation formulationsen
dc.typeTechnical Reporten
dc.contributor.departmentUniversity of Chesteren
refterms.dateFOA2018-08-13T21:58:14Z
html.description.abstractIn discussions of certain neutral delay differential equations in Hale’s form, the relationship of the original problem with an integrated form (an integral equation) proves to be helpful in considering existence and uniqueness of a solution and sensitivity to initial data. Although the theory is generally based on the assumption that a solution is continuous, natural solutions of neutral delay differential equations of the type considered may be discontinuous. This difficulty is resolved by relating the discontinuous solution to its restrictions on appropriate (half-open) subintervals where they are continuous and can be regarded as solutions of related integral equations. Existence and unicity theories then follow. Furthermore, it is seen that the discontinuous solutions can be regarded as solutions in the sense of Caratheodory (where this concept is adapted from the theory of ordinary differential equations, recast as integral equations).


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