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Abstract
Abstract

... This equation also has intrinsic interest in its own right. The main theorem - the Accident theorem–states, that under very mild conditions, solutions to this equation cannot happen by accident; that is, there are no singular solutions, but rather every solution belongs to a parametrizable class of ...
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Section 1.1 - Gordon State College

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Partial differential equation



In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (A special case are ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model.PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.
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