{"id":{"repo_id":"sevilla","oai_identifier":"oai:idus.us.es:11441/128907"},"canonical_url":"https://search.dev.ndltd.org/etd/sevilla/oai:idus.us.es:11441/128907","repository":{"repo_id":"sevilla","name":"Universidad de Sevilla","base_url":"https://idus.us.es/server/oai/request"},"display":{"title":"Singularly nonautonomous semilinear evolution equations with almost sectorial operators","abstract":"In this work we consider the singularly nonautonomous semilinear parabolic problem ut + A(t)u = F(u); t > ; u( ) = u0; in a Banach space X, where A(t); t 2 R, is a family of uniformly almost sectorial operators. The term singularly nonautonomous express the fact that the linear part of the equation, A(t) : D X ! X, is time-dependent and the almost sectoriality of the family A(t) comes from a deficiency in its resolvent estimate. For this semilinear problem in the abstract setting we study local well-posedness, regularity of the solution and the asymptotic dynamics of the problem. To illustrate the ideas developed for the abstract initial value problem, we consider a singularly nonautonomous reaction-diffusion equation in a domain with a handle. This type of domain consists in a subset of RN, 0 = [ R0, where is an open set of RN and R0 is diffeomorphic to a subset (0; 1) R. The “handle” refers to this line segment R0 attached to . In 0 we consider the following reaction-diffusion equation [equation]. This equation generates a singularly nonautonomous evolution equation with almost sectorial operator and local well-posedness, existence of strong solution and existence of pullback attractor are studied, in the lights of the abstract theory developed. In particular, in order to obtain existence of attractors, the system above will be decouple, originating two evolution equations: one with Neumann homogeneous boundary condition in and another with nonhomogeneous and time-dependent Dirichlet boundary conditions in R0. The properties of those two decoupled equations are thoughtfully studied and from them, estimates on the pullback attractor are obtained.","abstract_html":"In this work we consider the singularly nonautonomous semilinear parabolic problem ut + A(t)u = F(u); t &gt; ; u( ) = u0; in a Banach space X, where A(t); t 2 R, is a family of uniformly almost sectorial operators. The term singularly nonautonomous express the fact that the linear part of the equation, A(t) : D X ! X, is time-dependent and the almost sectoriality of the family A(t) comes from a deficiency in its resolvent estimate. For this semilinear problem in the abstract setting we study local well-posedness, regularity of the solution and the asymptotic dynamics of the problem. To illustrate the ideas developed for the abstract initial value problem, we consider a singularly nonautonomous reaction-diffusion equation in a domain with a handle. This type of domain consists in a subset of RN, 0 = [ R0, where is an open set of RN and R0 is diffeomorphic to a subset (0; 1) R. The “handle” refers to this line segment R0 attached to . In 0 we consider the following reaction-diffusion equation [equation]. This equation generates a singularly nonautonomous evolution equation with almost sectorial operator and local well-posedness, existence of strong solution and existence of pullback attractor are studied, in the lights of the abstract theory developed. In particular, in order to obtain existence of attractors, the system above will be decouple, originating two evolution equations: one with Neumann homogeneous boundary condition in and another with nonhomogeneous and time-dependent Dirichlet boundary conditions in R0. The properties of those two decoupled equations are thoughtfully studied and from them, estimates on the pullback attractor are obtained.","abstract_has_math":false,"creators":["Boldrin Belluzi, Maykel"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Caraballo Garrido, Tomás","Schiabel, Karina"],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-09-21","date_published":"2021-09-21","updated_at":"2026-07-24T04:29:54Z","subjects":[],"languages":["eng"],"rights":["Attribution-NonCommercial-NoDerivatives 4.0 Internacional"],"rights_urls":["http://creativecommons.org/licenses/by-nc-nd/4.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/11441/128907","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Caraballo Garrido, Tomás","Schiabel, Karina"]},{"key":"dc:creator","label":"Author","values":["Boldrin Belluzi, Maykel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2022-01-17T12:49:15Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-01-17T12:49:15Z"]},{"key":"dc:date.issued","label":"Date","values":["2021-09-21"]},{"key":"dc:type","label":"Dc Type","values":["doctoral thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Attribution-NonCommercial-NoDerivatives 4.0 Internacional"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://creativecommons.org/licenses/by-nc-nd/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/11441/128907"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this work we consider the singularly nonautonomous semilinear parabolic problem ut + A(t)u = F(u); t > ; u( ) = u0; in a Banach space X, where A(t); t 2 R, is a family of uniformly almost sectorial operators. The term singularly nonautonomous express the fact that the linear part of the equation, A(t) : D X ! X, is time-dependent and the almost sectoriality of the family A(t) comes from a deficiency in its resolvent estimate. For this semilinear problem in the abstract setting we study local well-posedness, regularity of the solution and the asymptotic dynamics of the problem. To illustrate the ideas developed for the abstract initial value problem, we consider a singularly nonautonomous reaction-diffusion equation in a domain with a handle. This type of domain consists in a subset of RN, 0 = [ R0, where is an open set of RN and R0 is diffeomorphic to a subset (0; 1) R. The “handle” refers to this line segment R0 attached to . In 0 we consider the following reaction-diffusion equation [equation]. This equation generates a singularly nonautonomous evolution equation with almost sectorial operator and local well-posedness, existence of strong solution and existence of pullback attractor are studied, in the lights of the abstract theory developed. In particular, in order to obtain existence of attractors, the system above will be decouple, originating two evolution equations: one with Neumann homogeneous boundary condition in and another with nonhomogeneous and time-dependent Dirichlet boundary conditions in R0. The properties of those two decoupled equations are thoughtfully studied and from them, estimates on the pullback attractor are obtained.","En este trabajo consideramos el problema parabólico semilineal singularmente no autónomo ut + A(t)u = F(u); t > ; u( ) = u0; en un espacio de Banach X, donde A(t); t 2 R, es una familia de operadores uniformemente casi sectoriales. El término singularmente no autónomo expresa el hecho de que la parte lineal de la ecuación, A(t) : DX ! X, es dependiente del tiempo y la casi sectorialidad de la familia A(t) proviene de una deficiencia en su estimación resolutiva. Para este problema semilineal en el entorno abstracto, estudiamos la buena postura local, la regularidad de la solución y la dinámica asintótica del problema. Para ilustrar las ideas desarrolladas para el problema abstracto de valor inicial, consideramos una ecuación de reacción-difusión singularmente no autónoma en un dominio con un mango. Este tipo de dominio consiste en un subconjunto de RN, 0 = [ R0, donde es un conjunto abierto de RN y R0 es difeomorfo a un subconjunto (0; 1) R. El \"mango\" se refiere a este segmento de línea R0 unido a . En 0 consideramos la siguiente ecuación de reacción-difusión 8>>>>>< >>>>>: wt div(a(t; x)rw) + w = f(w); x2; t > ; @w @n = 0; x 2 @ ; vt @r(a(t; r)@rv) + v = f(v); r2R0; t > ; v(p0) = w(p0) y v(p1) = w(p1): Esta ecuación genera una ecuación de evolución singularmente no autónoma con operador casi sectorial y bien posicionado local, se estudia la existencia de una solución fuerte y la existencia de un atractor pullback, a la luz de la teoría abstracta desarrollada. En particular, para obtener la existencia de atractores, se desacoplará el sistema anterior, originando dos ecuaciones de evolución: uno con condición de frontera homogénea de Neumann en y otro con condiciones de frontera de Dirichlet no homogéneas y dependientes del tiempo en R0. Las propiedades de esas dos ecuaciones desacopladas se estudian cuidadosamente y, a partir de ellas, se obtienen estimaciones sobre el atractor de retroceso."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Singularly nonautonomous semilinear evolution equations with almost sectorial operators"]}]}],"canonical_facts":{"dc:contributor.advisor":["Caraballo Garrido, Tomás","Schiabel, Karina"],"dc:creator":["Boldrin Belluzi, Maykel"],"dc:date.accessioned":["2022-01-17T12:49:15Z"],"dc:date.available":["2022-01-17T12:49:15Z"],"dc:date.issued":["2021-09-21"],"dc:description.abstract":["In this work we consider the singularly nonautonomous semilinear parabolic problem ut + A(t)u = F(u); t > ; u( ) = u0; in a Banach space X, where A(t); t 2 R, is a family of uniformly almost sectorial operators. The term singularly nonautonomous express the fact that the linear part of the equation, A(t) : D X ! X, is time-dependent and the almost sectoriality of the family A(t) comes from a deficiency in its resolvent estimate. For this semilinear problem in the abstract setting we study local well-posedness, regularity of the solution and the asymptotic dynamics of the problem. To illustrate the ideas developed for the abstract initial value problem, we consider a singularly nonautonomous reaction-diffusion equation in a domain with a handle. This type of domain consists in a subset of RN, 0 = [ R0, where is an open set of RN and R0 is diffeomorphic to a subset (0; 1) R. The “handle” refers to this line segment R0 attached to . In 0 we consider the following reaction-diffusion equation [equation]. This equation generates a singularly nonautonomous evolution equation with almost sectorial operator and local well-posedness, existence of strong solution and existence of pullback attractor are studied, in the lights of the abstract theory developed. In particular, in order to obtain existence of attractors, the system above will be decouple, originating two evolution equations: one with Neumann homogeneous boundary condition in and another with nonhomogeneous and time-dependent Dirichlet boundary conditions in R0. The properties of those two decoupled equations are thoughtfully studied and from them, estimates on the pullback attractor are obtained.","En este trabajo consideramos el problema parabólico semilineal singularmente no autónomo ut + A(t)u = F(u); t > ; u( ) = u0; en un espacio de Banach X, donde A(t); t 2 R, es una familia de operadores uniformemente casi sectoriales. El término singularmente no autónomo expresa el hecho de que la parte lineal de la ecuación, A(t) : DX ! X, es dependiente del tiempo y la casi sectorialidad de la familia A(t) proviene de una deficiencia en su estimación resolutiva. Para este problema semilineal en el entorno abstracto, estudiamos la buena postura local, la regularidad de la solución y la dinámica asintótica del problema. Para ilustrar las ideas desarrolladas para el problema abstracto de valor inicial, consideramos una ecuación de reacción-difusión singularmente no autónoma en un dominio con un mango. Este tipo de dominio consiste en un subconjunto de RN, 0 = [ R0, donde es un conjunto abierto de RN y R0 es difeomorfo a un subconjunto (0; 1) R. El \"mango\" se refiere a este segmento de línea R0 unido a . En 0 consideramos la siguiente ecuación de reacción-difusión 8>>>>>< >>>>>: wt div(a(t; x)rw) + w = f(w); x2; t > ; @w @n = 0; x 2 @ ; vt @r(a(t; r)@rv) + v = f(v); r2R0; t > ; v(p0) = w(p0) y v(p1) = w(p1): Esta ecuación genera una ecuación de evolución singularmente no autónoma con operador casi sectorial y bien posicionado local, se estudia la existencia de una solución fuerte y la existencia de un atractor pullback, a la luz de la teoría abstracta desarrollada. En particular, para obtener la existencia de atractores, se desacoplará el sistema anterior, originando dos ecuaciones de evolución: uno con condición de frontera homogénea de Neumann en y otro con condiciones de frontera de Dirichlet no homogéneas y dependientes del tiempo en R0. Las propiedades de esas dos ecuaciones desacopladas se estudian cuidadosamente y, a partir de ellas, se obtienen estimaciones sobre el atractor de retroceso."],"dc:format":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/11441/128907"],"dc:language.iso":["eng"],"dc:rights":["Attribution-NonCommercial-NoDerivatives 4.0 Internacional"],"dc:rights.uri":["http://creativecommons.org/licenses/by-nc-nd/4.0/"],"dc:title":["Singularly nonautonomous semilinear evolution equations with almost sectorial operators"],"dc:type":["doctoral thesis"]},"updated_at":"2026-07-24T04:29:54Z"}