dc.creator | Boldrin Belluzi, Maykel | es |
dc.creator | Caraballo Garrido, Tomás | es |
dc.creator | Nascimento, Marcelo J.D. | es |
dc.creator | Schiabel, Karina | es |
dc.date.accessioned | 2022-09-29T11:06:49Z | |
dc.date.available | 2022-09-29T11:06:49Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | Boldrin Belluzi, M., Caraballo Garrido, T., Nascimento, M.J.D. y Schiabel, K. (2022). Strong solutions for semilinear problems with almost sectorial operators. Journal of Evolution Equations, 22, 10-1-10-28. | |
dc.identifier.issn | 1424-3199 | es |
dc.identifier.issn | 1424-3202 | es |
dc.identifier.uri | https://hdl.handle.net/11441/137465 | |
dc.description.abstract | In this paper we study a semilinear parabolic problem
ut + Au = f(t, u), t > τ ; u(τ ) = u0 ∈ X,
in a Banach space X, where A : D(A) ⊂ X → X is an almost sectorial operator. This problem
is locally well-posed in the sense of mild solutions. By exploring properties of the semigroup
of growth 1 − α generated by −A, we prove that the local mild solution is actually strong
solution for the equation. This is done without requiring any extra regularity for the initial
condition u0 ∈ X and under suitable assumptions on the nonlinearity f. We apply the results
for a reaction-diffusion equation in a domain with handle where the nonlinearity f satisfies a
polynomial growth
|f(t, u) − f(t, v)| ≤ C|u − v|(1 + |u|
ρ−1 + |v|
ρ−1
)
and we establish values of ρ for which the problem still have strong solution.
Mathematical Subject Classification 2020: 35A01, 35D30, 35D35, 35K58
Key words and phrases: Almost sectorial operators, semigroups of growth 1 − α, semilinear
problems, strong solutions. | es |
dc.format | application/pdf | es |
dc.format.extent | 28 p. | es |
dc.language.iso | eng | es |
dc.publisher | Springer | es |
dc.relation.ispartof | Journal of Evolution Equations, 22, 10-1-10-28. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.title | Strong solutions for semilinear problems with almost sectorial operators | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis numérico | es |
dc.relation.publisherversion | https://doi.org/10.1007/s00028-022-00785-8 | es |
dc.identifier.doi | 10.1007/s00028-022-00785-8 | es |
dc.journaltitle | Journal of Evolution Equations | es |
dc.publication.volumen | 22 | es |
dc.publication.initialPage | 10-1 | es |
dc.publication.endPage | 10-28 | es |