Partial differential equation quasi linear

Vol. 1898 H.R. Beyer, Beyond Partial Differential Equations, On linear and Quasi-Linear Abstract Hyperbolic Evolution Equations (2007)... 

Rhee, Aris, and Amundson, First-Order Partial Differential Equations Volume 1. Theory and Application of Single Equations Volume 2. Theory and Application of Hyperbolic Systems of Quasi-Linear Equations, Prentice Hall, Englewood Cliffs, New Jersey, 1986,1989. 

The system of hyperbolic and parabolic partial differential equations representing the ID or 2D model of monolith channel is solved by the finite differences method with adaptive time-step control. An effective numerical solution is based on (i) discretization of continuous coordinates z, r and t, (ii) application of difference approximations of the derivatives, (iii) decomposition of the set of equations for Ts, T, c and cs, (iv) quasi-linearization of... 

A widespread concept of "mathematical physics equations includes primarily linear and quasi-linear partial differential equations. But what are "mathematical chemistry equations and "mathematical chemistry in general ... 

It is known [56] that an arbitrary system of quasi-linear partial differential equations which may be written in the form... 

This is a first-order, quasi-linear partial differential equation, although the presence of the maximization gives it an unconventional form. It must be integrated subject to the boundary condition... 

Equations (6) and (7) form a set of quasi-linear hyperbolic partial differential equations. A solution of the form ... 

Rhee et al. developed a theory of displacement chromatography based on the mathematical theory of systems of quasi-linear partial differential equations and on the use of the characteristic method to solve these equations [10]. The h- transform is basically an eqmvalent theory, developed from a different point of view and more by definitions [9]. It is derived for the stoichiometric exchemge of ad-sorbable species e.g., ion exchange), but as we have discussed, it can be applied as well to multicomponent systems with competitive Langmuir isotherms by introducing a fictitious species. Since the theory of Rhee et al. [10] is based on the use of the characteristics and the shock theories, its results are comprehensive e.g., the characteristics of the components that are missing locally are supplied directly by this theory, while in the /i-transform they are obtained as trivial roots, given by rules and definitions. 

The elementary theory concerning the character of partial differential equations has developed mainly from the study of the simplified two dimensional, quasi-linear second order equation defined by [55, 174] ... 

The solution of the quasi-Unear partial differential equations that govern the hydraulic transient problem is more challenging than the steady network solution. The Russian scientist Nikolai Zhukovsky offered a simplified arithmetic solution in 1904. Many other methods-graphical, algebraic, wave-plane analysis, implicit, and linear methods, as well as the method of characteristics-were introduced between the 1950 s and 1990 s. In 1996, Basha and his colleagues published another paper solving the hydraulic transient problem in a direct, noniterative fashion, using the mathematical concept of perturbation. 

The above quasi-linear partial differential equation can be solved by using equations based on the method of characteristics (Equations 5.84-5.88). 

The characteristic equations belonging to the quasi-linear partial differential equation (2.95) are... 

General first-order kinetics also play an important role for the so-called local eigenvalue analysis of more complicated reaction mechanisms, which are usually described by nonlinear systems of differential equations. Linearization leads to effective general first-order kinetics whose analysis reveals infomiation on the time scales of chemical reactions, species in steady states (quasi-stationarity), or partial equilibria (quasi-equilibrium) [M, and ]. 

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