In this paper we describe the asymptotic behavior of the positive solutions of a class of parabolic equations according to the size of a certain parameter. Within the range of values of the parameter where the model does not admit an attracting classical steady state it possesses an attracting metasolution ---a very weak generalized solution. It turns out that the minimal metasolution attracts all positive solutions starting in a subsolution and that the limiting profile of any other positive solution lies in the order interval defined by the minimal and the maximal metasolution.
"Dynamics of parabolic equations: from classical solutions to metasolutions." Differential Integral Equations 16 (7) 813 - 828, 2003. https://doi.org/10.57262/die/1356060598