Consider the PDE:


With boundary conditions:


Let $X(t,y,z)$ and $U(t,y,z)$ be the solutions to ODE Cauchy Problem:



With initial conditions:



  1. Show that the function implicitly given by


is a $C^1$ solution to the PDE for a small time

  1. Estimate the maximal time for which the solution given by point "1" be computed

How can I use the Implicit Function Theorem here in order to show point "1"?

  • 1
    $\begingroup$ Do you know what that theorem says? $\endgroup$ – Umberto P. Mar 13 at 19:26

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.