Roles of Weight Functions to a Nonlocal Porous Medium Equation with Inner Absorption and Nonlocal Boundary Condition

and Applied Analysis 3 He studied the asymptotic behavior of solutions and found the influence of weight function on the existence of global and blow-up solutions. Wang et al. 10 studied porous medium equation with power form source term ut Δu u, x, t ∈ Ω × 0, ∞ , 1.8 subjected to nonlocal boundary condition 1.2 . By virtue of the method of upper-lower solutions, they obtained global existence, blow-up properties, and blow-up rate of solutions. For the study of the initial boundary value problems for the parabolic equations with nonlocal terms which subjected to the weighted nonlocal linear boundary condition 1.2 , we refer to 11–16 . Lin and Liu 11 considered the semilinear parabolic equation