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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…
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…
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…