SOLUTIONS TO NONLINEAR RECOMBINATION EQUATION FOR INFINITE SPATIAL DOMAIN

Contemporary physical theories for the simultaneous diffusion and recombination of electrons and ions or free radicals feature a governing nonlinear parabolic equation of the concentration of the recombining species is continuous and the initial particle total is finite. It is shown that the total particle number is bounded below by a certain positive constant for any solution to the recombination equation in the infinite (unbounded) spatial domain such that the initial value is continuous and finite. Previously obtained generic results are specialized here to yield general forms which bound the concentration above and below. Finally, supplementary upper and lower bounds on the asymptotic total particle number are derived.