Spatial-time decay for nonlinear problems backward in time

The aim of this work is to provide spatial-time decay estimates for three backward-in-time nonlinear parabolic problems. To this end, we will impose several conditions on the nonlinear terms in order to obtain our estimates. It is worth noting that this type of conditions is satisfied for a large number of nonlinear problems. We will study three problems: the first two problems are of first order in time (when the nonlinearity is either in the gradient of the unknown or either it is given by the unknown), meanwhile the third one is of second order. Our results extend the ones obtained previously in the linear case.