Explore BrainMass
Share

Explore BrainMass

    Heat Equation Problem

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Find the solution u(x,t) of the heat equation:
    ut = 1/2 uxx

    (a) with initial data u(x,0) = x
    (b) with initial data u(x,0) = x^2
    (c) with initial data u(x,0) = sinx
    (d) with initial data u(x,0) = 0 x < 0 and u(x,0) = 1 or x >/= 0

    I know the solution of the heat equation with given initial data is unique. So if you happen to guess a function that satisfies the heat equation and satisfies initial condition, then it is a unique solution.

    © BrainMass Inc. brainmass.com October 10, 2019, 12:02 am ad1c9bdddf
    https://brainmass.com/math/numerical-analysis/heat-equation-problem-276554

    Solution Summary

    Heat equation problem is assessed in the solution.

    $2.19