| Texto completo | |
| Autor(es): |
Bezerra, Flank D. M.
;
Carvalho, Alexandre N.
;
Santos, Lucas A.
;
Takaessu Jr, Carlos R.
Número total de Autores: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE; v. 26, n. 2, p. 30-pg., 2025-01-01. |
| Resumo | |
In this paper we consider the ordinary differential equation of third order d(3)u/dt(3) + A(theta)d(2)u/dt(2) + A du/dt +Au = 0 <br /> where 0 <= theta< sigma <= 1 subject to initial conditions u(0) = u0 , du/dt|( t=0 ) (0) = u(1). d(2)u/dt(2)|( t=0 ) (0) =u(2) <br /> where X is a separable Hilbert space, A: D(A)subset of X -> X is an unbounded, linear, closed, densely-defined, self-adjoint and positive definite operator, and A(alpha): D(A(alpha)) subset of X -> X denotes the fractional power of A for a <euro> (0,1). We discuss the possibility of these problems being well posed (here well-posedness means that there is a strongly continuous semigroup associated to the equation) in a suitable phase space and for different choices of 0 <= theta < sigma <= 1 namely, theta+ sigma <= 1 (range for which the problem is not well posed), theta+ rho = 1 (range for which the problem may be well posed) and theta+ sigma> 1 (range where the problem may be well posed and the associated semigroup may be analytic). Moreover, we present an application of our results for evolutionary equations. (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: | 20/14075-6 - Sistemas dinâmicos e seus atratores sob perturbação |
| Beneficiário: | Alexandre Nolasco de Carvalho |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |