Optimal existence and uniqueness in a nonlinear diffusion–absorption equation with critical exponents

Abstract

We study the existence and uniqueness of non-negative solutions of the nonlinear parabolic equationposed in Q = RN × (0, ∞) with general initial data u(x, 0) = u0(x) ≧ 0. We find optimal exponential growth conditions for existence of solutions. Similar conditions apply for uniqueness, but the growth rate is different. Such conditions strongly depart from the linear case m = 1, ut = Δu – u, and also from the purely diffusive case ut = Δum.