Research on the reaction-diffusion equation with Robin and free boundary condition

Abstract The free boundary value problem of reaction-diffusion equation is studied. In the first chapter, Logistic diffusion with and main work this paper are introduced. second chapter preparation work, explaining existence uniqueness solution equation. third we prove that messages propagate or disappear in finite time by constructing asymptotic properties upper lower solutions. 4, criterion disappearance given, threshold information propagation given according to initial value. results show when larger than value, will whole region. Otherwise message stop propagating for a limited time.