Non-homogeneous reaction in a non-linear diffusion operator with advection to model a mass transfer process.
Abstract: It is the objective to provide a mathematical treatment of a nonhomogeneous
and non-lipschitz reaction problem with a non-linear diffusion
and advection operator, so that it can be applied to a fire extinguishing process
in aerospace. The main findings are related with the existence and characterization
of a finite propagation support that emerges in virtue of the the
non-linear diffusion formulation. It is provided a precise assessment on different
times associated to the extinguisher discharge process. Particularly, the
time required to activate the discharge, the time required for the extinguisher
front to cover the whole domain, the time required to reach a minimum level
of concentration so as to extinguish a fire and the time required by the agent
to reach some difficult dead zones where the extinguisher propagates only by
diffusion and no advection. The equation proposed is firstly discussed from a
mathematical perspective to find analytical solutions and propagating profiles.
Afterwards, the application exercise is introduced.
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