6 papers
The Cauchy problem for -evolution equations with initial data in Gelfand-Shilov spaces
Marco Cappiello, Eliakim Cleyton Machado
We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumpti…
Differential Complexes in Time-Periodic Gelfand-Shilov Spaces
Fernando de Ãvila Silva, Marco Cappiello, Alexandre Kirilov +1
We study the global solvability of a class of differential complexes on the product manifold associated with systems of evolution operators of th…
Smoothing effect for higher order dispersive equations and applications to nonlinear initial value problems
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
In this paper we deal with the initial value problem related to a family of dispersive inhomogeneous evolution equations Pu=f with variable coefficients belonging to the class of p…
Global Hypoellipticity for Systems in Time-Periodic Gelfand-Shilov Spaces
Fernando de Ãvila Silva, Marco Cappiello, Alexandre Kirilov
We investigate the global hypoellipticity of a class of overdetermined systems with coefficients depending both on time and space variables in the setting of time-periodic Gelfand-…
The Cauchy problem for -evolution equations with variable coefficients in Gevrey classes
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello +1
We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumpti…
Propagation of singularities for anharmonic Schrödinger equations
Marco Cappiello, Luigi Rodino, Patrik Wahlberg
We consider evolution equations for two classes of generalized anharmonic oscillators and the associated initial value problem in the space of tempered distributions. We prove that…