Global Existence and Blow-up of Solutions to a Quasilinear Parabolic Equation with Nonlocal Source and Nonlinear Boundary Condition - Cui, Zhoujin; Yu, Pinneng; Su, Huilin (Communications in Mathematics and Applications, 2012)
This paper investigates the behavior of positive solution to the following p-Laplacian equation align*u_t - (|u_x|^p-2u_x)_x = _0^a u^α(ξ,t)dξ+ku^β(x,t),(x,t)[0,a]×(0,T)align*with nonlinear boundary condition u_x|_x=0=0, u_x|_x=a=u^q|_x=a, where p≥ 2, α, β, k,q>0. The authors first get the local existence result by a regularization method. Then under appropriate hypotheses, the authors establish that positive weak solution either exists globally or blow up in finite time by using comparison principle.