Gevrey estimates of the resolvent and sub-exponential time-decay of solutions

In this article, we study a class of non-selfadjoint Schr{\"o}dinger operators H which are perturbation of some model operator H 0 satisfying a weighted coercive assumption. For the model operator H 0 , we prove that the derivatives of the resolvent satisfy some Gevrey estimates at threshold zero. As application, we establish large time expansions of semigroups e --tH and e --itH for t > 0 with subexponential time-decay estimates on the remainder, including possible presence of zero eigenvalue and real resonances

Large-time asymptotics of solutions to the Kramers-Fokker-Planck equation with a short-range potential

In this work, we use scattering method to study the Kramers-Fokker-Planck equation with a potential whose gradient tends to zero at the infinity. For short-range potentials in dimension three, we show that complex eigenvalues do not accumulate at low-energies and establish the low-energy resolvent asymptotics. This combined with high energy pseudospectral estimates valid in more general situations gives the large-time asymptotics of the solution in weighted $L^2$ spaces

Gevrey-Type Resolvent Estimates at the Threshold for a Class of Non-Selfadjoint Schrödinger Operators

In this article, we show that under some coercive assumption on the complex-valued potential V(x), the derivatives of the resolvent of the non-selfadjoint Schröinger operator H = −∆ + V(x) satisfy some Gevrey estimates at the threshold zero. As applications, we establish subexponential time-decay estimates of local energies for the semigroup e−tH, t > 0. We also show that for a class of Witten Laplacians for which zero is an eigenvalue embedded in the continuous spectrum, the solutions to the heat equation converges subexponentially to the steady solution

DIAGNOSIS OF THE COENOSIA MOLLICULA-GROUP (DIPTERA: MUSCIDAE), WITH DESCRIPTIONS OF FIVE NEW SPECIES FROM CHINA

The Coenosia mollicula-group from China is studied, and five new species are described: Coenosia albifronta Xue et Wang sp. n., Coenosia adrohalter Xue et Wang sp. n., Coenosia deciseta Xue et Wang sp. n., Coenosia latiaedeaga Xue et Wang sp. n. and Coenosia nigriceps Xue et Wang sp. n. A key for the identification of males of the 16 Chinese species are given