Явление мгновенной компактификации носителя в условиях неоднородной абсорбции и при возможном росте начальных данных

Abstract

We study the instantaneous support shrinking phenomenon for a doubly nonlinear degenerate parabolic equation with inhomogeneous absorption in the case of slow diffusion, when the initial Cauchy data are, in general, Radon measures and grow at infinity depending on the behavior of the absorption at infinity. For nonnegative solutions, we obtain the necessary and sufficient conditions for the instantaneous support shrinking phenomenon in terms of a local behavior of the array of initial data together with the behavior of the absorption. We also give the bilateral estimates exact with respect to order for the support size.