The steady temperature of a thin rectangular plate lying in the -plane obeys…

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

Mathematical Methods for Physics, Ch The classical partial differential equations of physics and their boundary conditions

Problem

The steady temperature of a thin rectangular plate lying in the xyxy-plane obeys Laplace's equation ∂x2T+∂y2T=0\partial_x^2T + \partial_y^2T = 0. ((a)) Write this equation in the form A ∂x2T+2B ∂x∂yT+C ∂y2T=0A\,\partial_x^2T + 2B\,\partial_x\partial_yT + C\,\partial_y^2T = 0, identify AA, BB, CC, compute B2−ACB^2-AC, and classify the equation. ((b)) State how many initial conditions the problem needs, and where boundary data must be supplied for the solution to be unique.

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