Explore BrainMass
Share

Explore BrainMass

    Partial Differential Equations

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

    1. Consider the first order PDE,

    ∂u/∂t = ct(∂u/∂x) -&#8734; < x < &#8734; c does not equal 0

    a) Find the fundamental solution

    b) Use the fundamental solution and convolution to find a formula for the solution to:

    ∂u/∂t = ct(∂u/∂x) -&#8734; < x < &#8734; c does not equal 0 u(x,0) = f(x)

    c) Use the method of characteristics to find the solution to part b.(Make sure your answers agree)

    © BrainMass Inc. brainmass.com October 9, 2019, 9:20 pm ad1c9bdddf
    https://brainmass.com/math/partial-differential-equations/partial-differential-equations-functions-180856

    Attachments

    Solution Preview

    Hello

    Please find the solution in the attached file.

    1. Consider the first order PDE,

    ∂u/∂t = ct(∂u/∂x) -∞ < x < ∞ c does not equal 0

    a) Find the fundamental solution

    b) Use the fundamental solution and convolution to find a formula for ...

    Solution Summary

    This finds the fundamental solution of a first-order partial differential equation, and uses that solution and convolution, as well as method of characteristics, in another problem. The expert uses the method of characteristics to find the function.

    $2.19