Robin gauge transform for constant drift
= Robin gauge transform for constant drift
{c}
Writing $u=e^{-\beta x/2}v$ transforms $u_t=u_{xx}+\beta u_x$ into $v_t=v_{xx}-\beta^2v/4$. A prescribed coordinate derivative $u_x=g$ at an endpoint becomes $v_x-(\beta/2)v=e^{\beta x/2}g$ there. Thus a <Neumann boundary condition> becomes a <Robin boundary condition>. The signs are coordinate-derivative signs at both endpoints; outward normal derivatives require a sign change at the left endpoint.