A weight-function approach for determining watershed initial conditions for combustion waves

In many generic combustion models, one finds that a combustion wave will de velop with a specific wave speed. However, there are possible initial tempe rature profiles which do not evolve into such waves, but rather die out to the ambient temperature. There can exist, in some models, a clear distincti on between those initial conditions that do evolve into combustion waves an d those that do not; this is sometimes referred to as the watershed initial condition. When fuel consumption is considered to be negligible, analytica l methods can be used to obtain the exact watershed. In this paper, we cons ider the problem of determining pseudo-watersheds and ascertaining the rela tionship between these pseudo-watersheds and the exact watersheds. In the p rocess a novel weight-function approach for infinite spatial domains is dev eloped.