A slab of copper conducts heat according to with

PHYSICS · Subjective · 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

A slab of copper conducts heat according to ∂tT=D ∂x2T\partial_t T = D\,\partial_x^2 T with D=1.1×10−4 m2 s−1D = 1.1\times10^{-4}\,\mathrm{m^2\,s^{-1}}. Write this equation in the general second-order linear form A ∂x2T+2B ∂x∂tT+C ∂t2T+(lower-order terms)=0A\,\partial_x^2T + 2B\,\partial_x\partial_tT + C\,\partial_t^2T + (\text{lower-order terms}) = 0 in the two variables xx and tt, identify AA, BB and CC, compute B2−ACB^2-AC, and state whether the equation is elliptic, parabolic or hyperbolic.

Browse the problem library