{"id":{"repo_id":"qucosa-diss","oai_identifier":"oai:qucosa:de:qucosa:71649"},"canonical_url":"https://search.dev.ndltd.org/etd/qucosa-diss/oai:qucosa:de:qucosa:71649","repository":{"repo_id":"qucosa-diss","name":"QUCOSA","base_url":"http://www.qucosa.de/oai/"},"display":{"title":"Global in time existence of Sobolev solutions to semi-linear damped sigma-evolution equations in L^q scales","abstract":"The main goal of this thesis is to prove the global (in time) existence of small data Sobolev solutions to semi-linear damped σ-evolution equations from suitable function spaces basing on L^q spaces by mixing additional L^m regularity for the data on the basis of L^q-L^q estimates for solutions, with q∈(1,∞) and m∈[1,q), to the corresponding linear models. To establish desired results, we would like to apply the theory of modified Bessel functions, Faà di Bruno's formula and Mikhlin-Hörmander multiplier theorem in the treatment of linear problems. In addition, some of modern tools from Harmonic Analysis play a fundamental role to investigate results for the global existence of small data Sobolev solutions to semi-linear problems. Finally, the application of a modified test function method is to devote to the proof of blow-up results for semi-linear damped σ-evolution models, where σ≥1 and δ∈[0,σ) are assumed to be any fractional numbers.","abstract_html":"The main goal of this thesis is to prove the global (in time) existence of small data Sobolev solutions to semi-linear damped σ-evolution equations from suitable function spaces basing on L^q spaces by mixing additional L^m regularity for the data on the basis of L^q-L^q estimates for solutions, with q∈(1,∞) and m∈[1,q), to the corresponding linear models. To establish desired results, we would like to apply the theory of modified Bessel functions, Faà di Bruno's formula and Mikhlin-Hörmander multiplier theorem in the treatment of linear problems. In addition, some of modern tools from Harmonic Analysis play a fundamental role to investigate results for the global existence of small data Sobolev solutions to semi-linear problems. Finally, the application of a modified test function method is to devote to the proof of blow-up results for semi-linear damped σ-evolution models, where σ≥1 and δ∈[0,σ) are assumed to be any fractional numbers.","abstract_has_math":false,"creators":["Dao, Tuan Anh"],"institution":"TU Bergakademie","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Reissig, Michael","Ebert, Marcelo","Picard, Rainer"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-08-04","date_published":"2020-08-04","updated_at":"2026-07-24T03:56:21Z","subjects":["sigma-evolution equations","damping terms","L^1 estimates","global existence","blow-up"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Reissig, Michael","Ebert, Marcelo","Picard, Rainer"]},{"key":"dc:creator","label":"Author","values":["Dao, Tuan Anh"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["TU Bergakademie Freiberg","Technische Universität Bergakademie Freiberg"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["TU Bergakademie","TU Bergakademie Freiberg"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["sigma-evolution equations","damping terms","L^1 estimates","global existence","blow-up"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The main goal of this thesis is to prove the global (in time) existence of small data Sobolev solutions to semi-linear damped σ-evolution equations from suitable function spaces basing on L^q spaces by mixing additional L^m regularity for the data on the basis of L^q-L^q estimates for solutions, with q∈(1,∞) and m∈[1,q), to the corresponding linear models. To establish desired results, we would like to apply the theory of modified Bessel functions, Faà di Bruno's formula and Mikhlin-Hörmander multiplier theorem in the treatment of linear problems. In addition, some of modern tools from Harmonic Analysis play a fundamental role to investigate results for the global existence of small data Sobolev solutions to semi-linear problems. Finally, the application of a modified test function method is to devote to the proof of blow-up results for semi-linear damped σ-evolution models, where σ≥1 and δ∈[0,σ) are assumed to be any fractional numbers."]},{"key":"dc:title","label":"Title","values":["Global in time existence of Sobolev solutions to semi-linear damped sigma-evolution equations in L^q scales"]}]}],"canonical_facts":{"dc:contributor":["Reissig, Michael","Ebert, Marcelo","Picard, Rainer"],"dc:creator":["Dao, Tuan Anh"],"dc:description.abstract":["The main goal of this thesis is to prove the global (in time) existence of small data Sobolev solutions to semi-linear damped σ-evolution equations from suitable function spaces basing on L^q spaces by mixing additional L^m regularity for the data on the basis of L^q-L^q estimates for solutions, with q∈(1,∞) and m∈[1,q), to the corresponding linear models. To establish desired results, we would like to apply the theory of modified Bessel functions, Faà di Bruno's formula and Mikhlin-Hörmander multiplier theorem in the treatment of linear problems. In addition, some of modern tools from Harmonic Analysis play a fundamental role to investigate results for the global existence of small data Sobolev solutions to semi-linear problems. Finally, the application of a modified test function method is to devote to the proof of blow-up results for semi-linear damped σ-evolution models, where σ≥1 and δ∈[0,σ) are assumed to be any fractional numbers."],"dc:publisher":["TU Bergakademie Freiberg","Technische Universität Bergakademie Freiberg"],"dc:subject":["sigma-evolution equations","damping terms","L^1 estimates","global existence","blow-up"],"dc:title":["Global in time existence of Sobolev solutions to semi-linear damped sigma-evolution equations in L^q scales"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["TU Bergakademie","TU Bergakademie Freiberg"]},"updated_at":"2026-07-24T03:56:21Z"}