Schrödingers Operators with Singular Magnetic Vector Potentials.
Series solutions of time-fractional PDEs by homotopy analysis method.
Smooth and discrete systems -- algebraic, analytic, and geometrical representations.
Solution of parabolic equations by means of Lyapunov functionals.
Solution of Partial Differential Equations by a Modified Random Walk.
Solving heat and wave-like equations using He's polynomials.
Stabilization of Schrödinger equation in exterior domains
We prove uniform local energy estimates of solutions to the damped Schrödinger equation in exterior domains under the hypothesis of the Exterior Geometric Control. These estimates are derived from the resolvent properties.
Sur un système d'équations aux dérivées partielles à une fonction d'ensemble comme inconnue
Symmetries of connections on fibered manifolds
The (infinitesimal) symmetries of first and second-order partial differential equations represented by connections on fibered manifolds are studied within the framework of certain “strong horizontal“ structures closely related to the equations in question. The classification and global description of the symmetries is presented by means of some natural compatible structures, eġḃy vertical prolongations of connections.