{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/53613"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/53613","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Stationary solutions of abstract kinetic equations","abstract":"The abstract kinetic equation Tψ’=-Aψ is studied with partial range boundary conditions in two geometries, in the half space x≥0 and on a finite interval [0, r]. T and A are abstract self-adjoint operators in a complex Hilbert space. In the case of the half space problem it is assumed that T is a (possibly) unbounded injection and A is a positive compact perturbation of the identity satisfying a regularity condition, while in the case of slab geometry T is a bounded injection and A is a bounded Fredholm operator with a finite dimensional negative part. Existence and uniqueness theory is developed for both models. Results are illustrated on relevant physical examples.","abstract_html":"The abstract kinetic equation Tψ’=-Aψ is studied with partial range boundary conditions in two geometries, in the half space x≥0 and on a finite interval [0, r]. T and A are abstract self-adjoint operators in a complex Hilbert space. In the case of the half space problem it is assumed that T is a (possibly) unbounded injection and A is a positive compact perturbation of the identity satisfying a regularity condition, while in the case of slab geometry T is a bounded injection and A is a bounded Fredholm operator with a finite dimensional negative part. Existence and uniqueness theory is developed for both models. Results are illustrated on relevant physical examples.","abstract_has_math":false,"creators":["Walus, Wlodzimierz Ignacy"],"institution":"Virginia Polytechnic Institute and State University","degree_name":"Ph. 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In the case of the half space problem it is assumed that T is a (possibly) unbounded injection and A is a positive compact perturbation of the identity satisfying a regularity condition, while in the case of slab geometry T is a bounded injection and A is a bounded Fredholm operator with a finite dimensional negative part. Existence and uniqueness theory is developed for both models. Results are illustrated on relevant physical examples."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. 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In the case of the half space problem it is assumed that T is a (possibly) unbounded injection and A is a positive compact perturbation of the identity satisfying a regularity condition, while in the case of slab geometry T is a bounded injection and A is a bounded Fredholm operator with a finite dimensional negative part. Existence and uniqueness theory is developed for both models. Results are illustrated on relevant physical examples."],"dc:description.degree":["Ph. D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/53613"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute and State University"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Stationary solutions of abstract kinetic equations"],"dc:type":["Dissertation"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. 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