Consider heat equation with a convection term
\begin{equation}
u_t+\underbracket{v u_x}_{\text{convection term}} =ku_{xx}.
\label{eq-HA3.4}
\end{equation}
a. Using change of variables $u(x,t)=U(x-vt,t)$ reduce it to ordinary heat equation and using (1)-(2) of
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{eq-HA3.4}) on $\{x>0,t>0\}$? Justify your answer.
