Partial differential equations linear second-order hyperbolic

The parts of Equation 1.54 are linear second-order hyperbolic partial differential equations called wave equations. The general solutions for the wave equations were given by D Alembert in 1747 [16] as... 

The theory for classifying linear, second-order, partial-differential equations is well established. Understanding the classification is quite important to understanding solution algorithms and where boundary conditions must be applied. Partial differential equations are generally classified as one of three forms elliptic, parabolic, or hyperbolic. Model equations for each type are usually stated as... 

The three-dimensional, second-order, nonlinear, elliptic partial differential equation may be simplified in the limit of weak electrolyte solutions, where the hyperbolic sine of is well approximated by 4). This yields the linearized Poisson—Boltzmann equation... 

Linear second-order partial differential equations in two independent variables are further classified into three canonical forms elliptic, parabolic, and hyperbolic. The general form of this class of equations is... 

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See also in sourсe #XX -- [ ]

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