4 citations · 6 across the 12 of their papers we have counts for
12 papers
Degenerate 3-evolution equations in Gevrey classes
Alexandre Arias Junior, Alessia Ascanelli
We consider the Cauchy problem for third-order evolution differential operators with variable coefficients, depending on time and space , where the lea…
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…
Schwartz very weak solutions for Schrödinger type equations with distributional coefficients
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello +1
This paper continues the analysis of Schrödinger type equations with distributional coefficients initiated by the authors in [3]. Here we consider coefficients that are tempered di…
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…
estimates for solutions to the plate equation with mass term
Alexandre Arias Junior, Halit Sevki Aslan, Antonio Lagioia +1
In this paper, we study the Cauchy problem for the linear plate equation with mass term and its applications to semilinear models. For the linear problem we obtain estima…
Schrödinger type equations with singular coefficients and lower order terms
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello +1
In this paper we investigate the well-posedness of the Cauchy problem for a Schrödinger operator with singular lower order terms. We allow distributional coefficients and we approa…
Some remarks on the Cauchy Problem for Schrödinger type equations in Gelfand-Shilov spaces
Alexandre Arias Junior
We consider the Cauchy problem for Schrödinger type operators. Under a suitable decay assumption on the imaginary part of the first order coefficients we prove well-posedness of th…
On the Cauchy problem for -evolution equations with variable coefficients: a necessary condition for Gevrey well-posedness
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
In this paper we consider a class of -evolution equations of arbitrary order with variable coefficients depending on time and space variables . We prove necessary conditi…
KdV-type equations in projective Gevrey classes
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
We prove well-posedness of the Cauchy problem for a class of third order quasilinear evolution equations with variable coefficients in projective Gevrey spaces. The class considere…
The Cauchy problem for a class of linear degenerate evolution equation on the torus
Alexandre Arias, Bruno de Lessa Victor
We study, in the periodic setting, the well-posedness of the Cauchy problem associated to the operator $P(t, D_{x}, D_{t}) = D_{t} - a_{2}(t) Δ_{x} + \sum_{j = 1}^{N} a_{1, j}(t) D…
Gevrey well posedness for -evolution equations with variable coefficients
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
We study the Cauchy problem for a class of third order linear anisotropic evolution equations with complex valued lower order terms depending both on time and space variables. Unde…
The Cauchy problem for -evolution equations with data in Gelfand-Shilov spaces
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
We consider the Cauchy problem for a -evolution operator with -depending coefficients and complex valued lower order terms. We assume the initial data to be Gevrey re…