In this paper we consider a class of evolution operators with coefficients depending on time
and space variables (t, x)∈ T× R n, where T is the one-dimensional torus, and prove …

In this paper, we investigate global properties of a class of evolution differential operators
defined on a product of tori and spheres. We present a comprehensive characterization of …

Let L=∂/∂ t+∑ j= 1 N (a j+ ibj)(t)∂/∂ xj be a vector field defined on the torus T N+ 1≃ R N+
1/2 π Z N+ 1, where aj, bj are real-valued functions and belonging to the Gevrey class G s (T …

We show that an obstruction of number-theoretical nature appears as a necessary condition
for the global hypoellipticity of the pseudo-differential operator L= D_t+ (a+ ib)(t) P (D_x) L …

In this note, we investigate Vekua-type periodic operators of the form P u= L u− A u− B u ̄,
where L is a constant coefficient partial differential operator. We provide a complete …

We study the finiteness of range's codimension for a class of non-globally hypoelliptic vector
fields on a torus of dimension three. The linear dependence of certain interactions of the …

A quasilinear autonomous system with an operator of differentiation with respect to the
characteristic directions of time and space variables associated with a Lyapunov's vector …

In this paper, we present necessary and sufficient conditions to have global analytic
hypoellipticity for a class of first-order operators defined on T 1× S 3. In the case of real …

In this paper we consider a class of evolution operators with coefficients depending on time
and space variables (t, x)∈ T× Rn, where T is the one-dimensional torus, and prove …

We proposed a self-oscillation control and its application to the locomotion of a robotic
snake system whose model is governed by a partial differential equation. The dynamics of …