On long-time behaviour of the positive solutions of nonhomogeneous non-Newtonian equation

Abstract

The subject of this investigation is the qualitative properties of positive solutions of the following nonhomogeneous equation

or, after the change v = u ^σ, of equation

in unbounded domain R ₊ × R^N , where the term g(s) is supposed to satisfy just a lower polynomial growth condition and g′(s) > −l ₁. The existence of the – global attractor for the equation (1′) is proved.

Keywords:

• nonlinear degenerate equation
• global attractor
• finite speed of propagation of perturbations

AMS Subject Classifications::

• 35B30
• 35B41
• 35K55