Regularity conditions (i.e. the Liu Smoller conditions) are necessary conditions that must be imposed on the equation of state of the multicomponent fluid in the limit of a vacuum state.
A similar partial boundary value condition was imposed on the equation begin{aligned} frac{partial v}{partial t}-operatorname{div} bigl(a(x) vert nabla v vert ^{p-2} nabla v bigr -sum_{i=1}^{N}bigr -sum_{i=1}^{x,t)v=f(x,t),quad (x,t) iN}b^{i}, end{aligned} (1.7) and a new approach to prescribe the boundary value condition rather than define the Fichera function was formulated by Yin and Wang [6].
The assumptions imposed on heat transfer equations and flow equations include non-isothermal flow, instantaneous local thermodynamic equilibrium, no change of heat transfer parameters, slightly compressible fluids and reservoir rocks, Darcy's law, no physical and chemical change and no hydrocarbon gases.
The advantage of this simulator was that we could be sure that no additional constraint was being imposed on the growth equations.
The advantage of this simulator was that it ensured that no additional constraint was being imposed on the growth equations, and that initial conditions were identical.
Further, the method used here permits us to relax the restrictions usually imposed on the coefficients of equation (1.1).
The boundary conditions imposed on the Fokker-Planck equation, as well as the Ψ V) term, are model-dependent.
In order to assure the existence of a unique solution of the nonlinear operator equation (2.15) in, some conditions must be imposed on the parameters appearing in the equation.
This is a result of the fixed limit that is imposed on the minimum optical gap (Equation 1), whereas in realistic systems, this will be less strict by participation of phonons in emission.
The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations.
