Global existence and blow-up of solutions of nonlocal diffusion problems with free boundaries |
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| Institution: | 1. Department of Mathematics, Faculty of Science and Technology, Keio University, Yokohama, Japan;2. Center for Advanced Intelligence Project, RIKEN, Tokyo, Japan;3. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia;1. School of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China;2. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, PR China |
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| Abstract: | In this paper, we investigate some nonlocal diffusion problems with free boundaries. We first give the existence and uniqueness of local solution by the ODE basic theory and the contraction mapping principle. Then we provide a complete classification for the global existence and finite time blow-up of solutions. Moreover, estimates of blow-up rate and blow-up time are also obtained for the blow-up solution. |
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| Keywords: | Nonlocal diffusion Free boundary Global existence Blow-up |
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