Well-posedness for degenerate third order equations with delay and applications to inverse problems
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Título
Well-posedness for degenerate third order equations with delay and applications to inverse problemsFecha de publicación
2018-10Editor
Springer; The Hebrew University Magnes PressCita bibliográfica
Conejero, J.A., Lizama, C., Murillo-Arcila, M. et al. Isr. J. Math. (2019) 229: 219. https://doi.org/10.1007/s11856-018-1796-8Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://link.springer.com/article/10.1007/s11856-018-1796-8#enumerationVersión
info:eu-repo/semantics/acceptedVersionPalabras clave / Materias
Resumen
In this paper, we study well-posedness for the following third-order in time equation with delay
(0.1)α(Mu′)′′(t)+(Nu′)′(t)=βAu(t)+γBu′(t)+Gu′t+Fut+f(t),t∈[0,2π]
where α, β, γ are real numbers, A and B are linear ... [+]
In this paper, we study well-posedness for the following third-order in time equation with delay
(0.1)α(Mu′)′′(t)+(Nu′)′(t)=βAu(t)+γBu′(t)+Gu′t+Fut+f(t),t∈[0,2π]
where α, β, γ are real numbers, A and B are linear operators defined on a Banach space X with domains D(A) and D(B) such that
D(A)∩D(B)⊂D(M)∩D(N);
u(t)is the state function taking values in X and ut: (−∞, 0] → X defined as ut(θ) = u(t+θ) for θ < 0 belongs to an appropriate phase space where F and G are bounded linear operators. Using operator-valued Fourier multiplier techniques we provide optimal conditions for well-posedness of equation (0.1) in periodic Lebesgue–Bochner spaces Lp(T,X), periodic Besov spaces Bsp,q(T,X) and periodic Triebel–Lizorkin spaces Fsp,q(T,X). A novel application to an inverse problem is given. [-]
Proyecto de investigación
Ministerio de Educación y Cultura, Spain (MTM2015-65825-P, MTM2016-75963-P, AICO/2016/30)Derechos de acceso
© Hebrew University of Jerusalem 2018
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