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Spectral analysis for some third-order differential equations: a semigroup approach

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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