Problems with free boundaries for nonlinear parabolic equations - Berezovsky, A. A.; Berezovs'kyi, M. A.; Mitropolskiy, Yu. A. (Ukrains’kyi Matematychnyi Zhurnal, 1997)
We establish necessary conditions for the existence of effects of space localization and stabilization in time that are qualitatively new for evolutionary equations. We suggest constructive methods for the solution of the corresponding one-dimensional problems with free boundaries that appear in ecology and medicine.