Isothermal combustion with two moving fronts (Q805905)

The combustion of porous solid occupying the half-space as it reacts irreversibly and isothermally with a gas diffusion through its pores yield the nondimensional problem: \[ C_{xx}=C^ p(1-X)^ m,\quad X_ t=C^ p(1-X)^ m,\quad X(x,0)=0,\quad C(0,t)=1,\quad C(\infty,t)=0 \] where C,S are gas and solid concentrations. It is shown that for \(m<1\) there is a conversion front \(x=\lambda (t)\) behind which the solid is fully converted but no such front exists for \(m\geq 1\). Also it is proved that the support of C(x,t) remains finite all if \(p<1\).