Global Existence and Large Time Asymptotic Bounds of $L^{infty}$ Solutions of Thermal Diffusive Combustion Systems on $R^n$

P. Collet, J. Xin

We consider the initial value problem for the thermal-diffusive combustion systems of the form: $u_{1,t}=Delt{a}_x{u}_1-u_1{u}_2^m$, $u_{2,t}=dDelt{a}_x{u}_2+u_1{u}_2^m$, $x in R…