The Rate of Spatial Decay of Nonnegative Solutions of Nonlinear Parabolic Equations and Inequalities
Let L be a uniformly parabolic linear partial differential operator. We show that nonnegative solutions of the differential inequality Lu ≤ c(u + ∇u|) on Rn x (0,T) for which u(x,T) = 0(exp(-δ|x|2)) must be identically zero if the constant δ is sufficiently large. An analogous result is given for nonlinear systems.
Proceedings of the American Mathematical Society
Lair, A. V. (1991). The rate of spatial decay of nonnegative solutions of nonlinear parabolic equations and inequalities. Proceedings of the American Mathematical Society, 112(4), 1077–1077. https://doi.org/10.1090/S0002-9939-1991-1059627-3