Abstract We consider time-frequency localization operators $$A_a^{\varphi _1,\varphi _2}$$ A a φ 1 , 2 with symbols a in the wide weighted modulation ...

In this paper we study the decay estimates of fourth order Schrödinger operator H=Δ2+V(x) on R2 with a bounded decaying potential V(x). We first deduce asymptotic expansions resolvent H near zero threshold in presence resonances or eigenvalue, and then use them to establish L1−L∞ e−itH generated by H. Our methods used depend Littlewood-Paley decomposition oscillatory integral theory. Moreover, ...

Abstract In this paper, we are interested in $L^{\infty }$ L ∞ decay estimates of weak solutions for the doubly nonlinear parabolic equation and degenerate evolution m -Laplacian not divergence form. By a modified Moser’s technique obtain solutiona.

We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in R3: ∂ttu− ∆u + m ∑ j=1 Vj (x− ~vjt)u = 0. The energy estimate and the local energy decay of a scattering state are also established. In order to study nonlinear multisoltion systems, we will present the inhomogeneous generalizations of Strichartz estimates ...