Existence theory for a class of evolutionary equations with time-lag, studied via integral equation formulations

Hdl Handle:
http://hdl.handle.net/10034/346601
Title:
Existence theory for a class of evolutionary equations with time-lag, studied via integral equation formulations
Authors:
Baker, Christopher T. H.; Lumb, Patricia M.
Abstract:
In 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).
Affiliation:
University of Chester
Citation:
Chester : University of Chester, 2006
Publisher:
University of Chester
Publication Date:
2006
URI:
http://hdl.handle.net/10034/346601
Additional Links:
http://www.chester.ac.uk
Type:
Technical Report
Language:
en
Series/Report no.:
Applied Mathematics Group Research Report; 2006 : 2
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorBaker, Christopher T. H.en
dc.contributor.authorLumb, Patricia M.en
dc.date.accessioned2015-03-13T13:19:01Zen
dc.date.available2015-03-13T13:19:01Zen
dc.date.issued2006en
dc.identifier.citationChester : University of Chester, 2006en
dc.identifier.urihttp://hdl.handle.net/10034/346601en
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).en
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
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