Classification of Partial Differential Equations and Canonical Forms
نویسنده
چکیده
where the coefficients A, B, and C are functions of x and y and do not vanish simultaneously, because in that case the second-order PDE degenerates to one of first order. Further, the coefficients D, E, and F are also assumed to be functions of x and y. We shall assume that the function u(x,y) and the coefficients are twice continuously differentiable in some domain Ω. The classification of second-order PDE depends on the form of the leading part of the equation consisting of the second order terms. So, for simplicity of notation, we combine the lower order terms and rewrite the above equation in the following form
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