{"id":{"repo_id":"qucosa-diss","oai_identifier":"oai:qucosa:de:qucosa:31787"},"canonical_url":"https://search.dev.ndltd.org/etd/qucosa-diss/oai:qucosa:de:qucosa:31787","repository":{"repo_id":"qucosa-diss","name":"QUCOSA","base_url":"http://www.qucosa.de/oai/"},"display":{"title":"Global in time existence and blow-up results for a semilinear wave equation with scale-invariant damping and mass","abstract":"The PhD thesis deals with global in time existence results and blow-up result for a semilinear wave model with scale-invariant damping and mass. Since the time-dependent coefficients for the considered model make somehow the damping and the mass a threshold term between effective and non-effective terms, it turns out that a fundamental role in the description of qualitative properties of solutions to this semilinear model and to the corresponding linear homogeneous Cauchy problem is played by the multiplicative constants appearing in those coefficients. For coefficients that make the damping term dominant, we can use the standard approach for the classical damped wave model with L^2 − L^2 estimates and the so-called test function method. On the other hand, when the interaction among those coefficients is balanced, then, it is possible to observe how typical tools for hyperbolic models, as for example Kato’s lemma, provide sharp global in time existence results and sharp blow-up results for super- and sub-Strauss type exponents, respectively.","abstract_html":"The PhD thesis deals with global in time existence results and blow-up result for a semilinear wave model with scale-invariant damping and mass. Since the time-dependent coefficients for the considered model make somehow the damping and the mass a threshold term between effective and non-effective terms, it turns out that a fundamental role in the description of qualitative properties of solutions to this semilinear model and to the corresponding linear homogeneous Cauchy problem is played by the multiplicative constants appearing in those coefficients. For coefficients that make the damping term dominant, we can use the standard approach for the classical damped wave model with L^2 − L^2 estimates and the so-called test function method. On the other hand, when the interaction among those coefficients is balanced, then, it is possible to observe how typical tools for hyperbolic models, as for example Kato’s lemma, provide sharp global in time existence results and sharp blow-up results for super- and sub-Strauss type exponents, respectively.","abstract_has_math":false,"creators":["Palmieri, Alessandro"],"institution":"TU Bergakademie Freiberg","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Reissig, Michael","Georgiev, Vladimir"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-12","date_published":"2018-09-12","updated_at":"2026-07-24T03:56:21Z","subjects":["Nonlinear wave equation","Scale-invariant coefficients","Global existence","Blow-up","Critical exponents"],"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","Georgiev, Vladimir"]},{"key":"dc:creator","label":"Author","values":["Palmieri, Alessandro"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["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 Freiberg"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Nonlinear wave equation","Scale-invariant coefficients","Global existence","Blow-up","Critical exponents"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The PhD thesis deals with global in time existence results and blow-up result for a semilinear wave model with scale-invariant damping and mass. Since the time-dependent coefficients for the considered model make somehow the damping and the mass a threshold term between effective and non-effective terms, it turns out that a fundamental role in the description of qualitative properties of solutions to this semilinear model and to the corresponding linear homogeneous Cauchy problem is played by the multiplicative constants appearing in those coefficients. For coefficients that make the damping term dominant, we can use the standard approach for the classical damped wave model with L^2 − L^2 estimates and the so-called test function method. On the other hand, when the interaction among those coefficients is balanced, then, it is possible to observe how typical tools for hyperbolic models, as for example Kato’s lemma, provide sharp global in time existence results and sharp blow-up results for super- and sub-Strauss type exponents, respectively."]},{"key":"dc:title","label":"Title","values":["Global in time existence and blow-up results for a semilinear wave equation with scale-invariant damping and mass"]}]}],"canonical_facts":{"dc:contributor":["Reissig, Michael","Georgiev, Vladimir"],"dc:creator":["Palmieri, Alessandro"],"dc:description.abstract":["The PhD thesis deals with global in time existence results and blow-up result for a semilinear wave model with scale-invariant damping and mass. Since the time-dependent coefficients for the considered model make somehow the damping and the mass a threshold term between effective and non-effective terms, it turns out that a fundamental role in the description of qualitative properties of solutions to this semilinear model and to the corresponding linear homogeneous Cauchy problem is played by the multiplicative constants appearing in those coefficients. For coefficients that make the damping term dominant, we can use the standard approach for the classical damped wave model with L^2 − L^2 estimates and the so-called test function method. On the other hand, when the interaction among those coefficients is balanced, then, it is possible to observe how typical tools for hyperbolic models, as for example Kato’s lemma, provide sharp global in time existence results and sharp blow-up results for super- and sub-Strauss type exponents, respectively."],"dc:publisher":["Technische Universität Bergakademie Freiberg"],"dc:subject":["Nonlinear wave equation","Scale-invariant coefficients","Global existence","Blow-up","Critical exponents"],"dc:title":["Global in time existence and blow-up results for a semilinear wave equation with scale-invariant damping and mass"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["TU Bergakademie Freiberg"]},"updated_at":"2026-07-24T03:56:21Z"}