On the Cauchy problem for the evolution p-Laplacian equations with gradient term and source

In this paper, the authors study the equation ut=div(Dup−2Du)+uq−1u−λDul in RN with p>2. We first prove that for 1 l p−1, the solution exists at least for a short time; then for , the existence and nonexistence of global (in time) solutions are studied in various situations