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Detail explanation 

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MAXIMUMU PRINCIPLES DIFFERENTIAL EQUATION

Mathematical modelling is used to describe physical, biological or chemical phenomena;one of the most common results of the modelling process is a system of ordinaryor partial differential equations. Finding and interpreting the solutions of these differentialequations is therefore a central part of applied mathematics, and a thorough understandingof differential equations is essential for any applied mathematician.One of the most useful and best known tools employed in the study of partial differential equations is the maximum principle. This principle is a generalization of the elementary fact of calculus that any function  which satisfies the inequality  on an interval  achieves its maximum value at one of the endpoints of the interval.More generally, functions which satisfy a differential inequality in a domain  and, because of it, achieve their maxima on the boundary of  are said to possess a maximum principle.

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Applied analysis and differential equations