Cauchy problem for doubly singular parabolic equation with gradient source |
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| Authors: | Haifeng Shang Junling Sun Lihua Deng |
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| Affiliation: | 1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, People's Republic of China;2. +86 391 3987138;3. +86 391 3987794 |
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| Abstract: | This paper examines the Cauchy problem for doubly singular parabolic equation with a source term depending solely on the gradient. We establish the local and global existence of solutions when initial data is merely a function in  ( ). Moreover, the uniform  ‐estimates and gradient estimates of solutions are obtained. |
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| Keywords: | Doubly singular parabolic equation Cauchy problem gradient source local and global existence 35K15 35K55 35K67 |
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