‎In this paper we focus on the Cauchy problem for the generalized‎ ‎IBq equation with damped term in $n$-dimensional space‎. ‎We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value‎, ‎provided that the initial value is suitably small‎. ‎Moreover‎, ‎we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...

the strong ground motions recorded during the 2002 avaj earthquake have been used to estimates wave attenuation, qβ, and spectral decay parameter, κ, for the avaj region. qβ for shear wave is estimatedas a function of frequency in the range of 0.6- 18 hz. the results show that qβ increases with frequency in theform of qβ=62.7 f 0.9. our estimates are within the estimated range for different par...

In this short note, we present some decay estimates for nonlinear solutions of 3d quintic, cubic NLS, and 2d quintic NLS (nonlinear Schrödinger equations).

In this work we study the Sobolev spaces generated by pseudo-differential operators associated with the group of symmetry of general first order hyperbolic systems. In these spaces we establish pointwise estimates of the solutions of a class of first order systems having convex eigenvalues. Various physical models belong to this class. For example, we consider crystal optics systems and anisotr...