  In these lecture notes, we address the problem of large-time asymptotic
behaviour of the solutions to scalar convection-diffusion equations set in
${R}^N$. The large-time asymptotic behaviour of the solutions to many
convection-diffusion equations is strongly linked with the behavior of the
initial data at infinity. In fact, when the initial datum is integrable and of
mass $M$, the solutions to the equations under consideration oftentimes behave
like the associated self-similar profile of mass $M$, thus emphasising the role
of scaling variables in these scenarios. However, these equations can also
manifest other asymptotic behaviors, including weakly non-linear, linear or
strongly non-linear behavior depending on the form of the convective term. We
give an exhaustive presentation of several results and techniques, where we
clearly distinguish the role of the spatial dimension and the form of the
nonlinear convective term.
  Translation (English) by Borjan Geshovski
