37 citations · 110 across the 23 of their papers we have counts for
5 papers · 1 filter
Exact splitting methods for kinetic and Schr{ö}dinger equations
Joackim Bernier, Nicolas Crouseilles, Yingzhe Li
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{ö}dinger type…
Exact splitting methods for semigroups generated by inhomogeneous quadratic differential operators
Joackim Bernier
We introduce some general tools to design exact splitting methods to compute numerically semigroups generated by inhomogeneous quadratic differential operators. More precisely, we…
Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects
Paul Alphonse, Joackim Bernier
We characterize geometrically the regularizing effects of the semigroups generated by accretive non-selfadjoint quadratic differential operators. As a byproduct, we establish the s…
Long time behavior of the solutions of NLW on the d-dimensional torus
Joackim Bernier, Erwan Faou, Benoit Grebert
We consider the non linear wave equation (NLW) on the d-dimensional torus with a smooth nonlinearity of order at least two at the origin. We prove that, for almost any mass, small…
Long-time behavior of second order linearized Vlasov-Poisson equations near a homogeneous equilibrium
Joackim Bernier, Michel Mehrenberger
The asymptotic behavior of the solutions of the second order linearized Vlasov-Poisson system around homogeneous equilibria is derived. It provides a fine description of some nonli…