We study the development of interfaces and qualitative behavior of solutions near the interfaces in a Cauchy problem for the nonlinear Fokker-Planck equation with reaction or absorption term. We concentrate our attention in the case when diffusion goes in the opposite direction of both the other forces, absorption and convection. In this situation, the interfaces may expand, shrink or remain stationary depending on the competition between these three factors. We focus on full classification of the problem on the initial development and asymptotics of the interfaces and local solutions near the interfaces for the reaction-diffusionconvection equation with compactly supported initial function. We apply significant methods rescaling , blow up techniques and comparison theorems in nonsmooth domains.
Volume 10 | 10-Special Issue
Pages: 1971-1993