The blow-up of solutions for [formula omitted]-Laplacian equations with variable sources under positive initial energy

Abstract

This paper deals with homogeneous Dirichlet boundary value problem to a class of m-Laplace equations with variable reaction ∂u∂t−div(|∇u|m−2∇u)=uq(x),x∈Ω,t>0, the bounded domain Ω⊂RN(N≥1) with a smooth boundary. We prove that the weak solutions of the above problems blow up in finite time for all q−>m−1(m≥2), when the initial energy is positive and initial data is suitably large. This result improves the recent result by Zhou and Yang (2015), which asserts the blow-up of solutions for N>m, provided that q+<Nm−m−NN−m.