It is well known, by now, that the three-dimensional non-viscous planetary geostrophic model, with vertical hydrostatic balance and horizontal Rayleigh friction, coupled to the heat diffusion and transport, is mathematically ill-posed. This is because the no-normal flow physical boundary condition implicitly produces an additional boundary condition for the temperature at the literal boundary. ...

objective: for the assessment of primary arch form, different methods have been used including qualitative classifications, inter-canine and inter-molar widths and quantitative and numerical methods using mathematical models. the purpose of this study was to compare the validity and reliability of cast analyzer x iranian software with those of curve expert professional version 1.1 for arch form...

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

<p style='text-indent:20px;'>In this paper, we study fractional subdiffusion fourth parabolic equations containing Caputo and Caputo-Fabrizio operators. The main results of the paper are presented in two parts. For first part with derivative, focus on global local well-posedness results. We mild solution for biharmonic heat equation derivative case globally Lipschitz source term. A new we...