Toronto Math Forum
APM3462015S => APM346Home Assignments => HA3 => Topic started by: Victor Ivrii on February 05, 2015, 07:27:12 PM

Consider heat equation with a convection term
\begin{equation}
u_t+\underbracket{v u_x}_{\text{convection term}} =ku_{xx}.
\label{eqHA3.4}
\end{equation}
a. Using change of variables $u(x,t)=U(xvt,t)$ reduce it to ordinary heat equation and using (1)(2) of http://www.math.toronto.edu/courses/apm346h1/20151/HA3.html (http://www.math.toronto.edu/courses/apm346h1/20151/HA3.html) for a latter write a formula for solution $u (x,t)$.
b. Can we use the method of continuation to solve IBVP with Dirichlet or Neumann boundary condition at $x>0$ for (\ref{eqHA3.4}) on $\{x>0,t>0\}$? Justify your answer.

Attached ;D

a Idea correct but it will be $(xvt)$ rather than $(x+vt)$