For 0 < α 1, N ⩾ 2 and with initial data ‖ u H + = ε, sufficiently small, we show that the existence time for solutions of fractional BBM equation ∂ t x | D 0, can be extended from hyperbolic 1 ε to . proof use a quasilinear modified energy method, based on normal form transformation as in Hunter, Ifrim, Tataru, Wong (Proc. Am. Math. Soc., 143(8) (2015) 3407–3412).

A derivation of the relation between the vacancy formation energy E,, the migration energy E, and the Debye temperature 0c is presented. In the Debye model, the relation between E, and Bc follows directly from the “dynamical” form of diffusion theories. The relation between E, and Bc is obtained for solids obeying a corresponding states law. The Debye temperature appearing in the derived expres...

‎in this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear pdes in mathmatical physics; namely the one-‎dimensional modified complex ginzburg-landau equation by using the $ (g^{'}/g) $ expansion method‎, homogeneous balance method, extended f-expansion method‎. ‎by ‎using homogeneous balance principle and the extended f-expansion, more periodic wave solutions expres...

We explore new routes for characterizing the Debye-like and α relaxation in 2-ethyl-1-hexanol (2E1H) monoalcohol by using low frequency dielectric techniques including thermally stimulated depolarization current (TSDC) techniques and isothermal depolarization current methods. In this way, we have improved the resolution of the overlapped processes making it possible the analysis of the data in ...