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Heat Equation, Boundary Conditions, Steady State Condition and Initial-Value Problem

(a) Find all the separated solutions of the attached heat equation (satisfying the attached boundary condition)

(b) Use these separated solutions to write a series solution for the initial value problem posed by the attached pde and the attached boundary conditions, with the initial condition given by {see attachment}

(c) Find the steady state solution for the inital value problem, taking into account the initial condition.

(d) Show that the series state solution for the initial value problem approaches the steady state solution of the initial value problem as {see attachment}

(e) Give a brief physical interpretation of this limiting behaviour as {see attachment}


Solution Summary

Heat Equations, Boundary Conditions, Steady State Conditions and an Initial-Value Problem are investigated. The solution is detailed and well presented.