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