Compactification of supports of energy weak solutions to quasilinear parabolic equations of nonstationary filtration type with strong convection (Q1585408)

The author studies some localization properties of weak solutions of the Cauchy problem for a wide class of quasilinear parabolic equations in the divergence form (including the equation describing non-Newtonian, nonlinear, non-stationary filtration with strong convection along the \(x_1\) axis). The main result states that a certain rate condition (as \(x_1\to\infty\)) imposed on the initial data ensures the instantaneous compactification (with or without time delay) of the support of an arbitrary solution of the Cauchy problem under consideration.