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On the Cauchy problem for the evolution p-Laplacian equations with gradient term and source
Authors:Songzhe Lian  Chunling Cao  Xiaojing Xu
Institution:a Institute of Mathematics, Jilin University, Changchun, Jilin 130012, PR China
b Institute of Applied Physics and Computational Mathematics, Beijing 100088, PR China
Abstract:In this paper, the authors study the equation ut=div(|Du|p−2Du)+|u|q−1uλl|Du| 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 View the MathML source, the existence and nonexistence of global (in time) solutions are studied in various situations.
Keywords:Cauchy problem  p-Laplacian equation  Gradient term  Blow-up
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