Distributed-order time-fractional wave equations appear in the modeling of propagation viscoelastic media. The material characteristics medium are modeled through constitutive functions or distributions distributed-order law. In this work we propose to take positive Radon measures for "functions". First, derive a thermodynamical restriction on which is easy check, and therefore suitable applica...

the development of the dynamical core of a potential-vorticity-based atmospheric general circulation model is explored. there are some advantages of using potential vorticity (pv) as a prognostic variable in that the resulting model can give more accurate simulation of the evolution of pv, as arguably the most fundamental dynamical quantity. further, there is possibility of explicit representat...

    M. and M.   Abstract: Existence and uniqueness of solution for singular 2-D systems depends on regularity condition. Simple regularity implies regularity and under this assumption, the generalized wave model (GWM) is introduced to cast singular 2-D system of equations as a family of non-singular 1-D models with variable structure.These index dependent models, along with a set of boundary co...

The variable order wave equation plays a major role in acoustics, electromagnetics, and fluid dynamics. In this paper, we consider the space-time variable order fractional wave equation with variable coefficients. We propose an effective numerical method for solving the aforementioned problem in a bounded domain. The shifted Jacobi polynomials are used as basis functions, and the variable-order...

We consider a model of nonlinear wave equations with periodically varying speed and periodic external forcing. By imposing non-resonance conditions on the frequency, we establish existence response solutions (i.e., same frequency as forcing) for such in Cantor set asymptotically full measure. The proof relies Lyapunov–Schmidt reduction together Nash–Moser iteration.