Front formation in an active scalar equation

We study the formation of thermal fronts in an active scalar equation that is similar to the Euler equation. For a particular initial condition, an ea rlier candidate for finite-time blowup, the front forms in a generalized se lf-similar way with constant hyperbolicity at the center. The behavior belo ngs to a class of scenarios for which finite-time blowup is impossible. A s ystematic exploration of many different initial conditions reveals no evide nce of singular solutions. [S1063-651X(99)10107-7].