Qunying Zhang, Jing Ge, Zhigui Lin
Abstract:
This article concerns with the solution to a heat equation with a free
boundary in n-dimensional space. By applying the energy inequality to the
solutions that depend not only on the initial value but also on the dimension
of space, we derive the sufficient conditions under which solutions blow up
at finite time. We then explore the long-time behavior of global solutions.
Results show that the solution is global and fast when initial value is small,
and the solution is global but slow for suitable initial value.
Numerical simulations are also given to illustrate the effect of the initial
value on the free boundary.
Submitted January 18, 2016. Published October 18, 2016.
Math Subject Classifications: 35K20, 35R35, 35K05.
Key Words: Free boundary; existence; blow-up; fast solution; slow solution.
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Qunying Zhang School of Mathematical Science Yangzhou University Yangzhou, Jiangxu 225002, China email: qyzhang@yzu.edu.cn |
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Jing Ge School of Mathematical Science Yangzhou University Yangzhou, Jiangxu 225002, China email: gejing2150@163.com |
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Zhigui Lin School of Mathematical Science Yangzhou University Yangzhou, Jiangxu 225002, China email: zglin68@hotmail.com |
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