A field on an anisotropic plate satisfies .

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Partial differential equations and boundary-value problems · Partial differential equations and boundary-value problems

Conditions of Validity, Ch The three equations, their characteristics and what makes a problem well posed

Problem

A field

u(x,y)

on an anisotropic plate satisfies

2u_{xx} - 5u_{xy} + 2u_{yy} = 0

. ((a)) Derive the characteristic directions (the slopes

\mathrm{d}y/\mathrm{d}x

of the characteristic curves). ((b)) State the classification of the equation (elliptic, parabolic or hyperbolic) and say what this implies about the type of data (initial-value or boundary-value) that would make the problem well posed.

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