Existence of a global attractor for a image-Laplacian equation in image Original Research Article

In this paper, we prove the existence of the (L2(Rn),W1,p(Rn)∩Lq(Rn))(L2(Rn),W1,p(Rn)∩Lq(Rn))-global attractor for the pp-Laplacian equation View the MathML sourceut−div(|∇u|p−2∇u)+λ|u|p−2u+f(u)=g with a more general nonlinear term f=f1+a(x)f2f=f1+a(x)f2 in RnRn, where a∈L1(Rn)∩L∞(Rn)a∈L1(Rn)∩L∞(Rn) and f1,f2f1,f2 satisfy the arbitrary qq-order polynomial growth condition without any restriction on View the MathML sourceq,p(q≥2,p>2).