Instantaneous Shrinking of Supports for Nonlinear Reaction-convection Equations

Abstract

Support analysis is performed for solutions of nonlinear reaction-convection equations in which both singular flux and source term are included. The positivity versus instantaneous shrinking for the solutions is determined by the relative strength of the flux and the source, as well as the decay rate at infinity of initial value of solutions. As an application of the analysis, the case of power-type nonlinearities is checked in details.