| Texto completo | |
| Autor(es): |
Bezerra, Flank D. M.
;
Santos, Lucas A.
;
Takaessu Jr, Carlos R.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | ASYMPTOTIC ANALYSIS; v. N/A, p. 14-pg., 2025-11-14. |
| Resumo | |
In this article, we present a spectral analysis for a class of abstract evolution equations of third order in time in order to study the well-posedness of these equations. Namely, we consider the following class of differential equations d 3 u d t 3 + a A 1 3 d 2 u d t 2 + b A 2 3 d u d t + c A u = 0 where a , b , c are non-negative constants, X is a Banach space, - A : D ( A ) subset of X -> X is the infinitesimal generator of an exponentially stable semigroup in X and A alpha denotes the fractional power of A . We determine, in terms of the coefficients a , b , c , when this equation is either ill-posed, or hyperbolic, or parabolic, in the sense of the theory of strongly continuous semigroups of bounded linear operators. Additionally, we present an example using the fractional Laplacian on a bounded smooth domain of R N . (AU) | |
| Processo FAPESP: | 20/14353-6 - Hiperbolicidade para problemas parabólicos quasilineares |
| Beneficiário: | Carlos Roberto Takaessu Junior |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |
| Processo FAPESP: | 22/02172-2 - Shadowing e hiperbolicidade para problemas parabólicos quasilineares |
| Beneficiário: | Carlos Roberto Takaessu Junior |
| Modalidade de apoio: | Bolsas no Exterior - Estágio de Pesquisa - Doutorado |
| Processo FAPESP: | 24/16879-6 - Shadowing Lemma em Sistemas Dinâmicos de Dimensão Infinita |
| Beneficiário: | Carlos Roberto Takaessu Junior |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |