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In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.
In mathematics, the Cauchy–Kovalevskaya theorem (also written as the Cauchy–Kowalevski theorem) is the main local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems. A special case was proven by Augustin Cauchy , and the full result by Sofya Kovalevskaya .
Download QR code; Print/export Download as PDF; Printable version; In other projects ... See also Nonlinear partial differential equation, List of partial ...
In the mathematical study of partial differential equations, Lewy's example is a celebrated example, due to Hans Lewy, of a linear partial differential equation with no solutions. It shows that the analog of the Cauchy–Kovalevskaya theorem does not hold in the smooth category.
The Kolmogorov backward equation (KBE) (diffusion) and its adjoint sometimes known as the Kolmogorov forward equation (diffusion) are partial differential equations (PDE) that arise in the theory of continuous-time continuous-state Markov processes. Both were published by Andrey Kolmogorov in 1931. [1]
F-Yang–Mills equations; Fast sweeping method; Fichera's existence principle; Field equation; Finite element method; Dynamic design analysis method; Finite water-content vadose zone flow method; First-order partial differential equation; KPP–Fisher equation; Fokas method; Föppl–von Kármán equations; Forward problem of electrocardiology ...
The series includes the volumes Mechanics, Mechanics of Deformable Bodies, Electrodynamics, Optics, Thermodynamics and Statistical Mechanics, and Partial Differential Equations in Physics. Focusing on one subject each semester, the lectures formed a three-year cycle of courses that Sommerfeld repeatedly taught at the University of Munich for ...
The general solution to the first order partial differential equation is a solution which contains an arbitrary function. But, the solution to the first order partial differential equations with as many arbitrary constants as the number of independent variables is called the complete integral. The following n-parameter family of solutions